6.1 Quantitative
1) Calculate the angular speed, in rad/s of a flywheel turning at 520.0 rpm.
- A) 54.44 rad/s
- B) 8.656 rad/s
- C) 40.83 rad/s
- D) 60.97 rad/s
Answer: A
Var: 50+
2) Through what angle in degrees does a 33 rpm record turn in 0.25 s?
- A) 50°
- B) 28°
- C) 36°
- D) 58°
Answer: A
Var: 26
3) An electrical motor spins at a constant 2857.0 rpm. If the armature radius is 2.685 cm, what is the acceleration of the edge of the rotor?
- A) 2403 m/s2
- B) 844.4 m/s2
- C) 241,100 m/s2
- D) 84.40 m/s2
Answer: A
Var: 50+
4) A satellite is in orbit around a planet. The orbital radius is 34.0 km and the gravitational acceleration at that height is 2.3 m/s2. What is the satellite’s orbital speed?
- A) 280 m/s
- B) 8.8 m/s
- C) 28 m/s
- D) 88 m/s
Answer: A
Var: 50+
5) A 23 kg mass is connected to a nail on a frictionless table by a (massless) string of length
1.3 m. If the tension in the string is 51 N while the mass moves in a uniform circle on the table, how long does it take for the mass to make one complete revolution?
- A) 4.8 s
- B) 3.8 s
- C) 4.5 s
- D) 5.2 s
Answer: A
Var: 50+
6) A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 13.2 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.
- A) 11.4 m/s
- B) 12.5 m/s
- C) 10.1 m/s
- D) 14.9 m/s
Answer: A
Var: 50+
7) A tetherball is on a 2.1 m string that makes an angle of 44° with the vertical as it moves around the pole in a horizontal plane. If the mass of the ball is 1.3 kg, what is the ball’s speed?
- A) 3.7 m/s
- B) 2.9 m/s
- C) 3.4 m/s
- D) 4.2 m/s
Answer: A
Var: 50+
8) In an amusement park ride, passengers stand inside an 8 m radius cylinder. Initially, the cylinder rotates with its axis oriented along the vertical. After the cylinder has acquired sufficient speed, it tilts into a vertical plane, that is, the axis tilts into the horizontal, as shown in the figure. Suppose that, once the axis has tilted into the horizontal, the ring rotates once every 4.5 s. If a rider’s mass is 40 kg, with how much force does the ring push on her at the top of the ride?
- A) 230 N
- B) 620 N
- C) 1000 N
- D) 390 N
Answer: A
Var: 50+
9) Future space stations will create an artificial gravity by rotating. Consider a cylindrical space station of 380 m diameter rotating about its axis. Astronauts walk on the inside surface of the space station. What rotation period will provide “normal” gravity?
- A) 28 s
- B) 39 s
- C) 6.2 s
- D) 4.4 s
Answer: A
Var: 50+
10) An aerobatic aircraft is to perform a spiral maneuver. If the engine provides a tangential acceleration of 5.41 m/s2, what is the radial acceleration it will experience at the end of a circle 30.8 m in radius, if the speed at the beginning of the stunt was 55.0 m/s?
- A) 166 m/s2
- B) 132 m/s2
- C) 98 m/s2
- D) 257 m/s2
Answer: A
Var: 50+
11) A ball of mass 8.0 kg is suspended by two wires from a horizontal arm, which is attached to a vertical shaft, as shown in the figure. The shaft is in uniform rotation about its axis such that the linear speed of the ball equals 2.3 m/s. The tension in wire 1 is closest to:
- A) 39 N
- B) 49 N
- C) 29 N
- D) 20 N
- E) 9.8 N
Answer: A
Var: 50+
12) The figure shows two wires tied to a 3.3 kg sphere that revolves in a horizontal circle at constant speed. At this particular speed the tension is the same in both wires. What is the tension?
- A) 24 N
- B) 32 N
- C) 44 N
- D) 22 N
Answer: A
Var: 50+
13) The figure shows two wires that are tied to a 710 g mass that revolves in a horizontal circle at a constant speed of 7.5 m/s. What is the tension in the upper wire?
- A) 34 N
- B) 20 N
- C) 27 N
- D) 41 N
Answer: A
Var: 50+
14) A 90 g bead on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the bead is at the very bottom of the circle is 2.2 N. A very sharp knife is suddenly inserted, as shown in the figure, to cut the string directly below the point of support. How far to the right of the center of the circle does the ball hit the floor?
- A) 160 cm
- B) 200 cm
- C) 240 cm
- D) 190 cm
Answer: A
Var: 40
15) The figure shows a 3.0 kg ball tied to the end of a 50 cm long string being swung in a circle in a vertical plane at constant speed. The center of the circle is h = 510 cm above the floor. The ball is swung at the minimum speed necessary to make it over the top without the string going slack. If the string is released at the instant the ball is at the top of the loop, how far to the right of the center of the circle does the ball hit the ground?
- A) 240 cm
- B) 230 cm
- C) 210 cm
- D) 0.0 cm
Answer: A
Var: 50+
16) What is the magnitude of the force exerted by Earth on the Moon?
- A) 2.01 × 1020N
- B) 7.67 × 1028N
- C) 2.01 × 1026N
- D) 7.67 × 1031N
Answer: A
Var: 1
17) An astronaut is in equilibrium when he is positioned 140 km from planet X and 581 km from planet Y, along the straight line joining the planets’ centers. What is the ratio of the masses X/Y?
- A) 0.0581
- B) 17.2
- C) 0.241
- D) 4.15
Answer: A
Var: 50+
18) At a given point above the surface of Earth, the gravitational acceleration is equal to 7.8 m/s2. The altitude of this point, above the surface of Earth, in km, is closest to:
- A) 770
- B) 970
- C) 1500
- D) 2000
- E) 2400
Answer: A
Var: 39
19) What is the gravitational force acting on a person due to another person standing 2 meters away? Assume each individual has 59 kg mass.
- A) 5.8 × 10-8 N
- B) 8.5 × 103 N
- C) 1.2 × 10-7 N
- D) 9.8 × 10-10 N
- E) 2.0 × 10-9 N
Answer: A
Var: 50+
20) The weight of spaceman Speff, solely due to the gravitational pull of planet X at its surface, is 389 N. If he moves to a distance of 1.86 × 104 km above the planet’s surface, his weight changes to 24.31 N. What is the mass of planet X, if Speff’s mass is 75 kg?
- A) 2.96 × 1024kg
- B) 2.96 × 1018kg
- C) 2.96 × 1017kg
- D) 1.59 × 1018kg
Answer: A
Var: 50+
21) If we assume that an electron is orbiting a proton just like the moon orbits Earth, find the electron’s orbital speed due to the gravitational attraction between itself and the proton. Take the orbital radius as 1.00 × 10-10 m. (This is a very wrong assumption to make.)
- A) 3.33 × 10-14m/s
- B) 1.11 × 10-13m/s
- C) 1.11 × 10-27m/s
- D) 1.06 × 10-27m/s
Answer: A
Var: 1
22) Spaceman Speff orbits planet X with his spaceship. To remain in orbit at 421 km from the planet’s center, he should maintain a speed of 80 m/s. What is the mass of planet X?
- A) 4.0 × 1019kg
- B) 5.1 × 1017kg
- C) 4.0 × 1016kg
- D) 5.1 × 1014kg
Answer: A
Var: 50+
23) From what height off the surface of Earth should an object be dropped to initially experience an acceleration of 0.5400 g?
- A) 2298 km
- B) 1689 km
- C) 5426 km
- D) 2930 km
Answer: A
Var: 46
24) Suppose we want a satellite to revolve around Earth 5 times a day. What should the radius of its orbit be? (Neglect the presence of the Moon.)
- A) 1.44 × 107m
- B) 0.69 × 107m
- C) 7.22 × 107m
- D) 2.11 × 107m
Answer: A
Var: 9
25) A proton moving at 0.999 of the speed of light orbits a black hole 4972 km from the center of the attractor. What is the mass of the black hole?
- A) 6.71 × 1033kg
- B) 6.71 × 1030kg
- C) 6.71 × 1036kg
- D) 6.71 × 1025kg
Answer: A
Var: 50+
26) You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 × 107 m. You have previously determined that the planet orbits 2.9 × 1011 m from its star with a period of 402 Earth days. Once on the surface you find that the acceleration due to gravity is 19.5 m/s2. What are the masses of (a) the planet and (b) the star?
- A) (a) 4 kg × 1025 kg
(b) 1.2 kg × 1031 kg
- B) (a) 3 kg × 1025 kg
(b) 1.2 kg × 1031 kg
- C) (a) 4 kg × 1025 kg
(b) 7.1 kg × 1030 kg
- D) (a) 3 kg × 1025 kg
(b) 7.1 kg × 1030 kg
Answer: A
Var: 50+
27) Find the orbital speed of an ice cube in the rings of Saturn, if the mass of Saturn is 5.67 x 1026 kg and the rings have an average radius of 100,000 km.
- A) 19.5 km/s
- B) 27.5 km/s
- C) 13.8 km/s
- D) 1.95 km/s
Answer: A
Var: 1
Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons.
28) In the table, the mass of Ekapluto is closest to:
- A) 1 × 1022kg
- B) 3 × 1022kg
- C) 1 × 1023kg
- D) 3 × 1023kg
- E) 1 × 1024kg
Answer: D
Var: 1
6.2 True/False
1) Satellites in orbit are accelerated toward Earth, so they must be getting closer and closer to our planet.
Answer: FALSE
Var: 1
2) Astronauts in orbiting satellites are weightless because they are so far from Earth that its gravitational pull is too weak to feel.
Answer: FALSE
Var: 1
3) If a highway curve is properly banked and posted at 45 mph, it is a good idea to drive somewhat below this speed if your tires are bald or if the road is icy.
Answer: FALSE
Var: 1
4) An ordinary car would not be able to go around an unbanked curve of a perfectly smooth road, no matter how the driver turned the wheels.
Answer: TRUE
Var: 1
5) If you swing a ball in a vertical circle using a thin string, at the bottom of the circle the tension in the string must be greater than the ball’s weight.
Answer: TRUE
Var: 1
6) Satellites in circular orbits around Earth are in equilibrium because they have uniform speed.
Answer: FALSE
Var: 1
7) While a Ferris wheel turns at uniform angular speed, a seat at the rim of the wheel has a nonzero radial acceleration toward the center of the wheel but a tangential acceleration of zero.
Answer: TRUE
Var: 1
8) If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out because an outward force balances the pull of gravity on the water.
Answer: FALSE
Var: 1
9) Earth’s gravity is caused by our planet’s spin on its axis.
Answer: FALSE
Var: 1
10) An Earth satellite needs to have its orbit changed so the new orbit will be twice as far from the center of Earth as the original orbit. The new orbital period will be twice as long as the original period.
Answer: FALSE
Var: 1
11) A satellite is orbiting Earth. If a payload of material is added until it doubles the satellite’s mass, Earth’s pull of gravity on this satellite will double but the satellite’s orbit will not be affected.
Answer: TRUE
Var: 1
12) Orbiting satellites accelerate toward Earth at 9.8 m/s2.
Answer: FALSE
Var: 1
13) If Earth had twice as much mass as it now does but were also twice its present diameter, the acceleration due to gravity at its surface would be the same as it is now.
Answer: FALSE
Var: 1
14) If the mass of Earth and all objects on it were suddenly doubled, the acceleration due to gravity at the surface would become 4 times what it is now.
Answer: FALSE
Var: 1
6.3 Conceptual
1) A mass on a string is swung in a vertical circle at a constant speed. The string will break if the tension in the string exceeds a critical value. At what part of the circle is the string most likely to break, and why?
Answer: The string is most likely to break at the lowest point in the circular path, because the tension in the string is greatest at this point. This follows from Newton’s Second Law:
= T – mg at the lowest point ⇒ T = + mg at the bottom of the arc.
Var: 1
2) A person ties a rock to a string and whirls it around in a vertical circle such that sometimes the rock is going straight upward and sometimes the rock is going straight down. She whirls the rock at the minimum speed (constant in time) such that the string is always taut (no sag). If she were to use a longer string, she would have to whirl the rock at a
- A) higher velocity.
- B) lower velocity.
- C) the same velocity.
Answer: A
Var: 1
3) A person ties a rock to a string and whirls it around in a vertical circle such that sometimes the rock is going straight upward and sometimes the rock is going straight down. She whirls the rock at the minimum speed (constant in time) such that the string is always taut (no sag). When is the tension the highest?
- A) It is highest when the rock is at the lowest elevation.
- B) It is highest when the rock is at the highest elevation.
- C) The tension is constant as the rock moves around in a circle.
Answer: A
Var: 1
4) A merry-go-round is spinning at a fixed rate. As a person is walking toward the edge,
- A) the force of static friction must increase in order for the person not to slide off.
- B) the force of static friction must decrease in order for the person not to slide off.
- C) the force of static friction such that the person does not slide off remains the same.
Answer: A
Var: 1
5) You need to make a sharp turn on a flat road, making a radius of curvature of 15 meters. How does the required force of static friction between your tires compare if you make the turn at 30 mph vs. 60 mph?
- A) The force of friction needs to be four times as large.
- B) The force of friction needs to be twice as large.
- C) The force of friction is the same for both speeds since the radius of curvature is the same.
- D) None of the above
Answer: A
Var: 1
6) If there is no such thing as a centrifugal force, why does someone in a car making a turn feel as if he or she is being pulled toward the outside of the curve?
Answer: The car is making a turn, but the person in the car is not part of the car. According to Newton’s First Law, you will move in a straight line until acted on by an outside force – thus, you move in a straight line while the car turns (at least until you run into the door. At this time, the car exerts a force on you, causing your direction of motion to change.).
Var: 1
7) Explain, from a force standpoint, why you need to reduce your normal driving speed around curves when it rains.
Answer: In order to safely negotiate a curve at a given velocity, frictional forces between the tires and the road must be large enough to provide the necessary centripetal force.
The coefficient of friction μ decreases when it rains, so the frictional force decreases.
Var: 1
8) How is it possible for someone to remain in her seat (without any straps) while upside down on a loop-the-loop roller coaster?
Answer: If the velocity of the roller coaster car is sufficiently large at the top of the loop, the person (and car) will remain on the track. For lower speeds, the normal force on the person goes to 0 before she reaches the top, meaning that she comes out of the seat.
(This follows from N = – mg.)
Var: 1
9) Astronauts in orbit are weightless, but they are not beyond the pull of Earth’s gravity. How can this be?
Answer: Astronauts in orbit are moving in uniform circular orbits; the centripetal force is provided by gravitational attraction. The net force experienced by an astronaut is 0, thus the astronaut is weightless. (The astronaut is in a continual state of free fall while in orbit.)
Var: 1
10) Can a satellite be in an elliptical orbit under uniform circular motion?
Answer: No. A satellite in an elliptical orbit would experience tangential acceleration. By definition, a satellite under uniform circular motion can have no tangential acceleration component. Therefore, its orbit can only be a circle.
Var: 1
11) If I set the car cruise control at a certain speed and take a turn, the speed will remain the same. So, why am I accelerating?
Answer: If you observe a car actually performing this maneuver, you will notice that the tires will skid at high speeds, or the car will bank in one side. This means that the car is actually accelerating, it is changing the one-dimensional speed to a two-dimensional velocity. But the speedometer cannot detect it. If you had a gyroscope on board, as airplanes do, it would register an acceleration.
Var: 1
12) In uniform circular motion we have an acceleration and the speed doesn’t change. But in projectile motion the speed does change under constant acceleration. Why are they both classified as uniform acceleration phenomena?
Answer: Acceleration is defined as the rate of change of velocity. Respecting this definition means that we observe the entire velocity vector’s behavior. Speed is only a constituent of velocity, therefore observing only the speed gives a partial and sometimes misleading picture of the physical phenomena. The fact is that in both cases the acceleration vector is uniform in a particular framework (coordinate system).
Var: 1
13) If you stood on a planet having a mass four times higher than Earth’s mass, and a radius two times longer than Earth’s radius, you would weigh
- A) the same as you do on Earth.
- B) two times more than you do on Earth.
- C) two times less than you do on Earth.
- D) four times more than you do on Earth.
Answer: A
Var: 1
14) A satellite having orbital speed V orbits a planet of mass M. If the planet had half as much mass, the orbital speed of the satellite would be:
- A) V
- B) 2V
- C) V
- D) V/
- E) V/2
Answer: D
Var: 1
15) A satellite of mass M takes time T to orbit a planet. If the satellite had twice as much mass, the time for it to orbit the planet would be:
- A) 4T
- B) 2T
- C) T
- D) T/2
- E) T/4
Answer: C
Var: 1
16) If the Moon were twice the distance from Earth than it currently is, the amount of time it would take to go around Earth would be roughly (the current orbital period of the Moon is four weeks)
- A) 11 weeks.
- B) eight weeks.
- C) six weeks.
- D) 88 weeks.
Answer: A
Var: 1
17) If an astronaut were exactly half way between Earth and the Moon, the net gravitational force exerted on the astronaut by these two objects would be
- A) directed toward Earth.
- B) zero.
- C) directed toward the Moon.
Answer: A
Var: 1
18) For astronauts in space, there is no atmosphere to slow their orbit. Why don’t they just fly away to the moon?
Answer: The astronauts were initially placed there by a capsule or shuttle. Therefore they have the same speed as the craft. If the craft was launched with enough energy to make a certain orbit, the extra energy must be gotten elsewhere. If the astronaut pushes hard enough on the craft, he will convert part of the work into kinetic energy and fly away. The problem is that to cover the distance in some kind of realistic time travel, he would have to push harder than a Titan.
Var: 1
College Physics, 2e (Knight)
Chapter 7 Rotational Motion
7.1 Quantitative
1) A child is sitting on the outer edge of a merry-go-round that is 18 m in diameter. If the merry-go-round makes 4.9 rev/min, what is the velocity of the child in m/s?
- A) 4.6 m/s
- B) 9.2 m/s
- C) 0.7 m/s
- D) 3.2 m/s
Answer: A
Var: 50+
2) Through what angle in degrees does a 33 rpm record turn in 0.32 s?
- A) 63°
- B) 35°
- C) 46°
- D) 74°
Answer: A
Var: 26
3) An electrical motor spins at a constant 2695.0 rpm. If the armature radius is 7.165 cm, what is the acceleration of the edge of the rotor?
- A) 5707 m/s2
- B) 281.6 m/s2
- C) 572,400 m/s2
- D) 28.20 m/s2
Answer: A
Var: 50+
4) At time t = 0 s, a wheel has an angular displacement of zero radians and an angular velocity of +28 rad/s. The wheel has a constant acceleration of -0.51 rad/s2. In this situation, the time t, at which the wheel comes to a mandatory halt, is closest to:
- A) 130 s
- B) 120 s
- C) 96 s
- D) 78 s
- E) 55 s
Answer: A
Var: 50+
5) A wheel accelerates from rest to 59 rad/s at a rate of 74 rad/s2. Through what angle (in radians) did the wheel turn while accelerating?
- A) 24 rad
- B) 19 rad
- C) 48 rad
- D) 30 rad
Answer: A
Var: 50+
6) A 95 N force exerted at the end of a 0.50 m long torque wrench gives rise to a torque of
15 N · m. What is the angle (assumed to be less than 90°) between the wrench handle and the direction of the applied force?
- A) 18°
- B) 14°
- C) 22°
- D) 25°
Answer: A
Var: 50+
7) A 0.18 m radius pulley is free to rotate about a horizontal axis. A 4.2 kg mass and a 8.0 kg mass are attached by a massless string, which is hung over the pulley. If the string does not slip, calculate the magnitude of the net torque on the pulley about its rotational axis.
- A) 6.7 N ∙ m
- B) 5.5 N ∙ m
- C) 7.6 N ∙ m
- D) 9.5 N ∙ m
Answer: A
Var: 46
8) A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 38 rad/s. The wheel is run at that angular velocity for 30 s and then power is shut off. The wheel slows down uniformly at 2.1 rad/s2 until the wheel stops. In this situation, the angular acceleration of the wheel between t = 0 s and t = 10 s is closest to:
- A) 3.8 rad/s2
- B) 4.6 rad/s2
- C) 5.3 rad/s2
- D) 6.1 rad/s2
- E) 6.8 rad/s2
Answer: A
Var: 50+
9) A torque of 12 N ∙ m is applied to a solid, uniform disk of radius 0.50 m. If the disk accelerates at 5.7 rad/s2, what is the mass of the disk?
- A) 17 kg
- B) 13 kg
- C) 8.5 kg
- D) 4.3 kg
Answer: A
Var: 50+
10) A particular motor can provide a maximum of 110.0 N · m of torque. Assuming that all of this torque is used to accelerate a solid, uniform flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to 6.04 rad/s?
- A) 2.47 s
- B) 2.10 s
- C) 2.99 s
- D) 3.24 s
Answer: A
Var: 50+
11) A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 96 rad/s. The wheel is run at that angular velocity for 40 s and then power is shut off. The wheel slows down uniformly at 1.5 rad/s2 until the wheel stops. In this situation, the time interval of deceleration is closest to:
- A) 64 s
- B) 62 s
- C) 66 s
- D) 68 s
- E) 70 s
Answer: A
Var: 50+
12) A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 29 rad/s. The wheel is run at that angular velocity for 27 s and then power is shut off. The wheel slows down uniformly at 2.7 rad/s2 until the wheel stops. In this situation, the average angular velocity in the time interval from t = 0 s to t = 25 s is closest to:
- A) 17 rad/s
- B) 15 rad/s
- C) 13 rad/s
- D) 11 rad/s
- E) 8.7 rad/s
Answer: A
Var: 50+
13) A solid, uniform sphere of mass 2.0 kg and radius 1.7 m rolls without slipping down an inclined plane of height 7.0 m. What is the angular velocity of the sphere at the bottom of the inclined plane?
- A) 5.8 rad/s
- B) 9.9 rad/s
- C) 11.0 rad/s
- D) 7.0 rad/s
Answer: A
Var: 50+
14) A solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane. If the angular velocity of the disk is 5.35 rad/s at the bottom, what is the height of the inclined plane?
- A) 5.61 m
- B) 4.21 m
- C) 4.94 m
- D) 6.73 m
Answer: A
Var: 50+
15) The table shows the masses and the coordinates x and y of a set of three point masses in the x-y plane. The masses are interconnected by light struts, forming a rigid body. The moment of inertia of the rigid body, through the center of mass and perpendicular to the x-y plane, is closest to:
- A) 3000 kg ∙ m2
- B) 3200 kg ∙ m2
- C) 3400 kg ∙ m2
- D) 3600 kg ∙ m2
- E) 3800 kg ∙ m2
Answer: E
Var: 1
16) A potter’s wheel (a solid, uniform disk) of mass 7.0 kg and radius 0.65 m spins about its central axis. A 2.1 kg lump of clay is dropped onto the wheel at a distance 0.41 m from the axis. Calculate the rotational inertia of the system.
- A) 1.8 kg ∙ m2
- B) 1.5 kg ∙ m2
- C) 0.40 kg ∙ m2
- D) 2.5 kg ∙ m2
Answer: A
Var: 31
17) A bicycle heading west at 2.0 m/s turns 90.0° to the left in 10.0 s. The final velocity of the bicycle after the turn is 4.2 m/s to the south. Find the direction of the wheel’s average angular acceleration. Express your answer as an angle relative to east.
- A) 25° south of east
- B) 25° north of east
- C) 65° north of east
- D) 65° south of east
Answer: A
Var: 46
18) A force in the +y direction applied at the point x = 2.3 m, y = 1.4 m gives rise to a torque of 71 N · m about the origin. Find the magnitude of the force.
- A) 31 N
- B) 51 N
- C) 71 N
- D) 87 N
Answer: A
Var: 46
19) A solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane. If the angular velocity of the disk is 4.27 rad/s at the bottom, what is the height of the inclined plane?
- A) 3.57 m
- B) 2.68 m
- C) 3.14 m
- D) 4.28 m
Answer: A
Var: 50+
20) A force of 17 N is applied to the end of a 0.63 m long torque wrench at an angle 45° from a line joining the pivot point to the handle. What is the magnitude of the torque generated about the pivot point?
- A) 7.6 N∙m
- B) 10.7 N∙m
- C) 12.0 N∙m
- D) 9.7 N∙m
Answer: A
Var: 12
21) A force of 16.88 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular acceleration of 1.20 rad/s2. Calculate the rotational inertia of the wheel.
- A) 4.78 kg ∙ m2
- B) 3.59 kg ∙ m2
- C) 5.98 kg ∙ m2
- D) 7.17 kg ∙ m2
Answer: A
Var: 50+
22) A light triangular plate OAB is in a horizontal plane. Three forces, F1 = 2 N, F2 = 4 N, and F3 = 7 N, act on the plate, which is pivoted about a vertical axis through point O. In the figure, consider the counterclockwise sense as positive. The sum of the torques about the vertical axis through point O, acting on the plate due to forces F1, F2, and F3, is closest to:
- A) 2.2 N ∙ m
- B) 2.6 N ∙ m
- C) -2.2 N ∙ m
- D) -2.6 N ∙ m
- E) zero
Answer: A
Var: 50+
23) A rectangular sign h = 20.0 cm high and w = 11.0 cm wide loses three of its four support bolts and rotates into the position as shown, with P1 directly over P3. It is supported by P2, which is so tight it holds the sign from further rotation. Find the gravitational torque about P2, if the mass of the sign is 5.0 kg.
- A) 4.7 Nm
- B) 2.6 Nm
- C) 0.27 Nm
- D) 0.48 Nm
Answer: A
Var: 50+
24) A particular motor can provide a maximum of 110.0 N · m of torque. Assuming that all of this torque is used to accelerate a solid, uniform flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to 8.13 rad/s?
- A) 3.33 s
- B) 2.83 s
- C) 4.03 s
- D) 4.36 s
Answer: A
Var: 50+
25) In the figure, a mass of 35.30 kg is attached to a light string that is wrapped around a cylindrical spool of radius 10 cm and moment of inertia 4.00 kg · m2. The spool is suspended from the ceiling, and the mass is then released from rest a distance 3.50 m above the floor. How long does it take to reach the floor?
- A) 2.97 s
- B) 2.85 s
- C) 0.892 s
- D) 4.18 s
- E) 5.89 s
Answer: A
Var: 50+
26) At time t = 0 s, a wheel has an angular displacement of zero radians and an angular velocity of +14 rad/s. The wheel has a constant acceleration of -0.41 rad/s2. In this situation, the time at which the angular displacement is + 88 rad and decreasing is closest to:
- A) 61 s
- B) 34 s
- C) 7 s
- D) 6 s
- E) 74 s
Answer: A
Var: 50+
7.2 True/False
1) There must be equal amounts of mass on either side of the center of mass.
Answer: FALSE
Var: 1
2) If you deform an object, you do not change its mass but you may change its moment of inertia and the location of its center of mass.
Answer: TRUE
Var: 1
3) If a spinning object has a negative angular acceleration, it must be slowing down.
Answer: FALSE
Var: 1
4) If two objects have the same moment of inertia, they must have the same mass.
Answer: FALSE
Var: 1
5) A cylinder and a sphere, both solid and uniform and having the same mass and diameter, roll without slipping down the same ramp starting from rest. Both of them will reach the ground at the same time.
Answer: FALSE
Var: 1
7.3 Conceptual
1) A small mass is placed on a record turntable that is rotating at 45 rpm. The linear acceleration of the mass is
- A) directed perpendicular to the line joining the mass and the center of rotation.
- B) independent (in magnitude) of the position of the mass on the turntable.
- C) greater the closer the mass is to the center.
- D) greater the farther the mass is from the center.
- E) zero.
Answer: D
Var: 1
2) In the figure are scale drawings of four objects, each of the same mass and uniform thickness. Which has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing? In each case the axis passes through point P.
- A) A
- B) B
- C) C
- D) D
- E) The moment of inertia is the same for all of these objects.
Answer: B
Var: 1
3) In the figure, a given force F is applied to a rod in several different ways. In which case is the torque due to F about the pivot P greatest?
- A) 1
- B) 2
- C) 3
- D) 4
- E) 5
Answer: A
Var: 1
4) A disk and a sphere are released simultaneously at the top of an inclined plane. They roll down without slipping. Which will reach the bottom first?
- A) the one of smallest diameter
- B) the one of greatest mass
- C) the disk
- D) the sphere
- E) They will reach the bottom at the same time.
Answer: D
Var: 1
5) A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), it’s velocity with respect to the road is
