Chapter 8 Physics

A 10 kg solid cylinder with a 50.0 cm radius has a moment of inertia of 1/2 MR2. If a torque of 2.0 N•m is applied to the object, the angular acceleration is

1.6 rad/s^2

A 4.00 kg mass is located at (2.00 m, 2.00 m, 0.00 m) and a 3.00 kg mass is located at (−1 m, 3.00 m, 0.00 m). The rotational inertia of this system of masses about the Y-axis, perpendicular to the X-Z plane, is

19 kg m ^2

A 5.00 kg mass is located at (2.00 m, 0.00 m, 0.00 m) and a 3.00 kg mass is located at (0.00 m, 4.00 m, 0.00 m). The center of gravity of the system of masses is

(1.25 m, 1.50 m, 0).

An 8.0 kg object has a moment of inertia of 1.00 kg m2. What torque is needed to give the object an angular acceleration of 1.5 rad/s2?

** 1.5 N*m

A 5.00 kg object has a moment of inertia of 1.20 kg m2. What torque is needed to give the object an angular acceleration of 2.0 rad/s2?

** 2.4 N*m

A 3.00 kg hollow sphere of radius 5.00 cm starts from rest and rolls without slipping down a 15.0 degree incline. If the length of the incline is 100 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is

*** 1.74 m/s

A uniform disk of mass 5.10 kg has a radius of 0.100 m and spins with a frequency of 0.550 rev/s. What is its angular momentum?

.0881 kg*m^2/s

An ice dancer with her arms stretched out starts into a spin with an angular velocity of 1.00 rad/s. Her moment of inertia with her arms stretched out is 2.48 kg m2. What is the increase in her rotational kinetic energy when she pulls in her arms to make her moment of inertia 1.40 kg m2?

.957 J

A 1.500 m long uniform beam of mass 30.00 kg is supported by a wire as shown in the figure. The beam makes an angle of 10.00 degrees with the horizontal and the wire makes an angle of 30.00 degrees with the beam. A 50.00 kg mass, m, is attached to the end of the beam. What is the tension in the wire?

1,255 N

A 4.00 kg hollow cylinder of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline. If the length of the incline is 50.0 cm, then the velocity of the center of mass of the cylinder at the bottom of the incline is

1.57 m/s

An ice dancer with her arms stretched out starts into a spin with an angular velocity of 1.00 rad/s. Her moment of inertia with her arms stretched out is 2.48 kg m2. What is her angular velocity when she pulls in her arms to make her moment of inertia 1.40 kg m2?

1.77 rad/s

What is the rotational inertia of a solid iron disk of mass 41.0 kg with a thickness of 5.00 cm and radius of 30.0 cm, about an axis perpendicular to the disk and passing through its center?

1.85 kg m^2

A thin rod is pivoted around its end, and an identical rod around its center. If they are to have the same rotational kinetic energy, then ωend/ωcenter =

1/2

A particle of mass m is rotating about a fixed point at a distance r. The angular speed of the particle is ω. What is the rotational kinetic energy of the particle?

1/2mr^2ω^2

A 2.00 m long horizontal uniform beam of mass 20.0 kg is supported by a wire as shown in the figure. The wire makes an angle of 20.0 degrees with the beam. Attached to the beam 1.40 m from the wall is a ball with a mass of 40.0 kg. What is the tension in the string?

1090 N

A 30.0 cm wrench is used to generate a torque at a bolt. A force of 50.0 N is applied at the end of the wrench at an angle of 70.0 degrees. The torque generated at the bolt is

14.1 N*m

A 100 kg solid spherical rock (I = 2/5 MR2) has a diameter of 50.0 cm. The rock is rolling down a hill with a velocity of 5.00 m/s. The total kinetic energy (angular + translational) of the rolling rock is

1750 J

A pole-vaulter holds out a 4.75 m pole horizontally in front of him. Assuming the pole is uniform in construction, and that he holds the pole with one hand at the very end, and one hand 0.75 m from the end, what is the ratio of the force applied by the hand on the end of the pole to the weight of the pole?

2.2

A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 20.0 cm and a moment of inertia of ½ MR2. If m1 is 3.00 kg, m2 is 6.00 kg and M is 4.00 kg, then what is the magnitude of the acceleration of the masses?

2.67 m/s^2

Jim and Mary are carrying Bob on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 80 N. Bob weighs 600 N. Bob's center of gravity is 80 cm from Mary. Jim and Mary are at the ends of the stretcher. The upward force that Jim is exerting to support the stretcher, with Bob on it, is

280 N

A 4.00 kg solid sphere of radius 5.00 cm starts from rest and rolls without slipping down a 30.0 degree incline. The acceleration of the center of mass of the solid sphere is

3.5 m/s^2

A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25.0 cm and a moment of inertia of ½ MR2. If m1 is 1.00 kg, m2 is 2.00 kg, and M is 4.00 kg, then what is the tension in the string attached to m2?

3.92 m/s^2

A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 30.0 cm and a moment of inertia of MR2. If m1 is 4.00 kg, m2 is 3.00 kg and M is 6.00 kg, then what is the tension in the string that is attached to m1?

36.2 N

A 4.00 kg solid sphere (I = 2/5 MR2) is spinning with an angular velocity of 23.0 rad/s. The diameter of the sphere is 20.0 cm. The rotational kinetic energy of the spinning sphere is

4.23 J

A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 20.0 cm and a moment of inertia of ½ MR2. If m1 is 3.00 kg, m2 is 6.00 kg and M is 4.00 kg, then what is the tension in the string that is attached to mass m2?

42.8 N

A 10 kg solid cylinder (I = 1/2 MR2) with a radius of 30.0 cm is rotating about a vertical axis through its center. If the angular momentum is increasing at the rate of 25.0 kg m2/s2, then what is the angular acceleration?

55.6 rad/s^2

Chris and Jamie are carrying Wayne on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 100 N. Wayne weighs 800 N. Wayne's center of gravity is 75.0 cm from Chris. Chris and Jamie are at the ends of the stretcher. The upward force that Chris is exerting to support the stretcher, with Wayne on it, is

550 N

A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). The rotational inertia of this system of masses about the Z-axis, perpendicular to the X-Y plane, is

68 kg m^2

A centrifuge has a rotational inertia of 5.50 × 10−3 kg m2. How much energy must be supplied to bring it from rest to 500 rad/s?

688 J

A 10 kg sphere with a 25.0 cm radius has a moment of inertia of 2/5 MR2. If a torque of 2.0 N•m is applied to the object, the angular acceleration is

8 rad/s ^2

A 20.0 cm wrench is used to generate a torque at a bolt. A force of 50 N is applied at the end of the wrench at an angle of 60.0 degrees to the wrench. The torque generated at the bolt is

8.7 N*m

A torque of 15.0 N.m is applied to a bolt. The bolt rotates through an angle of 360 degrees. The work done in turning the bolt is

94.2 J

A 6.00 kg mass is located at (2.00 m, 2.00 m, 2.00 m) and a 5.00 kg mass is located at (−1.0 m, 3.00 m, −2.00 m). The rotational inertia of this system of masses about the Z-axis, perpendicular to the X-Y plane, is

98 kg m^2

Identify the statements that are true regarding torque.

Torque can be positive, negative, or zero. The SI units of torque are N⋅m.

A system in equilibrium cannot have

a non-zero acceleration

A turntable must spin at 33.3 rev/min (3.49 rad/s) to play an old-fashioned vinyl record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 1.90 revolutions, starting from rest? The turntable is a uniform disk of diameter 30.5 cm and mass 0.260 kg.

.00154 N*m

A bicycle wheel, of radius 0.300 m and mass 1.30 kg (concentrated on the rim), is rotating at 4.00 rev/s. After 51.0 s the wheel comes to a stop because of friction. What is the magnitude of the average torque due to frictional forces?

.058 N*m

A 2.00 kg solid sphere (I = 2/5 MR2) with a diameter of 50.0 cm is rotating at an angular velocity of 5.0 rad/s. The angular momentum of the rotating sphere is

.25 kg m^2/s

What is the rotational inertia of a solid iron disk of mass 34.0 kg, with a thickness of 5.00 cm and radius of 13.5 cm, about an axis through its center and perpendicular to it?

.309825 kg*m^2

A 0.50 kg solid disk spins at 250 rpm. A torque of 12.5 N·m is applied for 0.150 s to bring it to rest. What is the disk's radius?

.54 m

A solid cylinder (mass 0.310 kg, radius 2.00 cm) rolls without slipping at a speed of 5.00 cm/s. What is its total kinetic energy?

.58 mJ

The rod of length a is free to rotate about an axis through the center. Five forces of equal magnitude F are acting on the rod as shown. What is the net torque on the rod about the axle?

0

A uniform thin rod of mass M and length L rotates about an axle through its center of mass at an angular acceleration due to a force applied at one end of the rod. If the length of the rod and the magnitude of the applied force were both doubled and the force still acted at one end of the rod, then by what factor would the magnitude of the angular acceleration change? Assume that the mass of the rod is constant.

1

Rank, in descending order, the given examples according to the mechanical advantage. Place the example with the largest mechanical advantage at the top and the smallest at the bottom.

1. a person pried the sewer lid 2. a person lifts a statue in a wheel barrow 3. a person cracks a walnut with pliers

Rank the following situations involving a solid sphere free to rotate about a line passing through its center according to the magnitude of its angular momentum, with the largest angular momentum magnitude at the top and the smallest at the bottom.

1. m = m, r = 3r, ang. accel. mag. = a 2. m = 2m, r = 2r, ang. accel. mag. = a 3. m = 2m, r = r, ang. accel. mag. = 2a 4. m = 3m, r = r, ang. accel. mag. = a

Rank the following situations involving a solid sphere free to rotate about a line passing through its center according to the magnitude of the net torque, with the largest net torque magnitude at the top and the smallest at the bottom.

1. m = m, r = 3r, ang. accel. mag. = a 2. m = 2m, r = 2r, ang. accel. mag. = a 3. m = 2m, r = r, ang. accel. mag. = 2a 4. m = 3m, r = r, ang. accel. mag. = a

A 4.00 kg hollow sphere (I = 2/3 MR2) is spinning with an angular velocity of 10.0 rad/s. The diameter of the sphere is 20.0 cm. The rotational kinetic energy of the spinning sphere is

1.33 J

The axis of rotation of an object passes perpendicularly through its center. Find the approximate length of the lever arm if a force is applied at a location 2 meters directly above the center of the object and in a direction down and to the left at a 45-degree angle below the horizontal.

1.41 m

A 20.0 cm wrench is used to generate a torque at a bolt. A force of 50 N is applied perpendicularly at the end of the wrench. The torque generated at the bolt is

10 N* m

An object that weighs 1160 N rests on a lever at a point 0.330 m from a support. On the same side of the support, at a distance of 3.00 m from it, an upward force with magnitude F is applied. Ignore the weight of the board itself. If the system is in equilibrium, what is F? Express your answer in Newtons.

127.6 N

A 10 kg object has a moment of inertia of 1.25 kg m2. If a torque of 2.5 N•m is applied to the object, the angular acceleration is

2.0 rad/s^2

The axis of rotation of an object passes perpendicularly through its center. What is the approximate length of the lever arm if a force is applied at a location 4 meters directly above the center of the object and in a direction up and to the left at a 45-degree angle above the horizontal?

2.83 m

Which of the following forces produces a torque with the largest magnitude? Assume that each force is applied at the same perpendicular distance from the axis of rotation.

20 N tangenitially

An unpowered pottery wheel is rotating at 30 rpm. If a blob of clay is dropped straight down on the wheel, increasing the moment of inertia of the system by 50%, what is the angular speed of the wheel after the clay lands on it.

20 rpm

A uniform log is rolling down hill without slipping and picking up speed. If the center of mass acceleration is 3.12 m/s2, and the radius is 15 cm, what is the angular acceleration?

20.8 rad/s^2

A propeller is spun up from rest to 1500 rpm in 15.0 s under the influence of a constant torque. If the work done by the engine in giving the propeller its final angular velocity is 25 kJ, what is the torque supplied by the engine?

21 N*m

A skater is initially spinning at a rate of 11.0 rad/s with a rotational inertia of 3.10 kg·m2 when her arms are extended. What is her angular velocity after she pulls her arms in and reduces her rotational inertia to 1.60 kg·m2?

21.3125 rad/s

The radius of a wheel is 0.770 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.00 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. How much work is done by the rope on the wheel during 1.00 revolution?

24.2 J

A 10 kg solid cylinder (I = 1/2 MR2) with a radius of 30.0 cm is rotating about a vertical axis through its center. If the angular momentum is increasing at the rate of 25 kg m2/s2, then what is the torque?

25 N*m

A 20.0 kg hollow cylinder (I = MR2) has a diameter of 50.0 cm. The cylinder is rolling down a hill with a velocity of 5.00 m/s. The rotational kinetic energy of the rolling cylinder is

250 J

A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). The rotational inertia of this system of masses about the X-axis, perpendicular to the Z-Y plane, is

36 kg m^2

The radius of a wheel is 0.770 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.00 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. How much rope unwinds while the wheel makes 1.00 revolution?

4.84 m

Jim and Mary are carrying Bob on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 80 N. Bob weighs 600 N. Bob's center of gravity is 80 cm from Mary. Jim and Mary are at the ends of the stretcher. The upward force that Mary is exerting to support the stretcher, with Bob on it, is

400 N

An irregularly shaped object is attached to an axle so that it may be spun. If a torque of 250 N·m must be applied for 1.25 s in order to give it a rotation period of 0.10 s, what is its moment of inertia?

5.0 Kg m^2

A grinding wheel has a mass of 250 kg and moment of inertia of 500 kg m2. A torque of 100 N•m is applied to the grinding wheel. If the wheel starts from rest, what is the angular momentum of the wheel after 5.0 seconds?

500 kg m^2/s

The radius of a wheel is 0.770 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.00 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. What is the angular displacement Δθ, in radians, of the wheel during 1.05 revolution?

60.60 rad

A trap door, of length and width 1.80 m, is held open at an angle of 65.0° with respect to the floor. A rope is attached to the raised edge of the door and fastened to the wall behind the door in such a position that the rope pulls perpendicularly to the trap door. If the mass of the trap door is 16.6 kg, what is the torque exerted on the trap door about the hinge by the rope? Enter a positive value if the torque is in counterclockwise direction and enter a negative value if the torque is in clockwise direction.

61.88 N*m

A light rod is being used as a lever as shown. The fulcrum is 1.20 m from the load and 2.40 m from the applied force. If the load has a mass of 13.1 kg, what force must be applied to lift the load?

64.19 N

Planet X orbits a star in the Andromeda galaxy. When planet X is closest to the star, the distance between the center of the planet and the center of the star is 1.5 x 1011 m and the planet's orbital speed is 50,000 m/s. What is the distance between their centers when the planet's orbital speed is 10,000 m/s? Assume that the star is stationary at all times.

7.5 x 10^11 m

The distance from the center of the breastbone to a man's hand, with the arm outstretched and horizontal to the floor, is 1.00 m. The man is holding a 9.09-kg dumbbell, oriented vertically, in his hand, with the arm horizontal. What is the torque due to this weight about a horizontal axis through the breastbone perpendicular to his chest?

89.082 N*m

An electron is moving with uniform circular motion around a circle of radius 6 cm. Its initial rotational kinetic energy is 24 J. If its (translational) speed doubled and it kept moving around the same circle, then how much rotational kinetic energy would it have?

96 J

Select all of the following objects that are in equilibrium (both translational and rotational).

A metal bar not spinning and oriented horizontally when its center of mass is at rest A wheel spinning at constant angular velocity when its center of mass is moving at constant translational velocity

A cube rests on a flat surface. If the flat surface is inclined at an angle of 45 degrees with respect to the horizontal, then where is the point of application of the contact forces between the cube and the flat surface?

At the lower corner of the cube that is in contact with the flat surface

Three particles, each undergoing circular motion about a fixed point, are shown in the image. In each case, the mass of the particle, the radius of the circle, and the angular velocity are indicated on the diagrams. Rank the three cases according to the rotational kinetic energy, from largest at the top to smallest at the bottom.

C A B

Rank the following with the largest torque magnitude at the top and the smallest at the bottom. The torque is exerted by the force about an axis passing perpendicularly through the point marked with a dot in the diagrams. All of the forces have the same magnitude.

C D A B

Four rods of mass m and length a are free to rotate about one end. The directions of the forces change when the rods rotate such that they remain perpendicular to the rod at all times. Rank the work done by the torque in each of the cases, with the largest work at the top and the smallest at the bottom.

D C A B

The dumbbell shown consists of two masses m and 2m connected by a light plastic rod. It is free to rotate at angular speed ω about the axes perpendicular to the plane of the dumbbell at the five points A through E shown (denoted by the × mark). Rank the points according to the rotational kinetic energy of the dumbbell about the five points, from largest at the top to smallest at the bottom.

E D A C B

A solid disk, a hoop, and a block of ice, each of the same mass, are one at a time placed at the same spot on an incline and released. The disk and hoop roll without slipping, but treat the block of ice as though it were frictionless. Choose all the true statements.

Each has the same kinetic energy at the bottom of the incline. The block has the greatest center of mass speed at the bottom of the incline.

The structure shown is constructed from three identical pieces of metal. Which of the following rankings of the moments of inertia of the structure about the four axes A through D is correct?

IA = ID > IC > IB

A disk is rotating freely about an axis that passes perpendicularly through its center at a constant angular speed. Two ants of equal mass suddenly drop onto the edge of the disk and get stuck to the rotating disk. What happens to the angular speed of the rotating disk?

It decreases, but not to zero.

A small object is connected to a rigid rod of negligible mass. The small object is free to rotate about a line that passes perpendicularly through the other end of the rigid rod. If the mass of the small object doubles and the length of the rigid rod stays the same, then what happens to the moment of inertia of the small object?

It doubles

Select all of the following statements that are always true.

It is impossible to exert a nonzero torque without exerting a nonzero force. If every force is zero, then the every torque is zero as well.

Most objects in orbit travel in elliptical orbits, so that their distance to the object they are orbiting is constantly changing. Match how each quantity changes when the orbiting object is closest to the object being orbited. Instructions

Orbital speed matches Greatest Moment of inertia matches Least Angular Momentum matches Unchanged

A ring of radius a, a thin rod of length 2a, and a disk of radius a are rotating about their centers of mass at a constant angular velocity. All three objects have the same mass M. Match the objects on the left with the magnitude of their angular momenta on the right.

Ring - Ma^2ω Thin rod - (1/3)Ma^2ω Disk - (1/2)Ma^2ω

Select all of the following that are true regarding the average power due to a constant torque.

The average power can be positive, negative, or zero. The average power is directly proportional to the magnitude of the torque. The average power is directly proportional to the magnitude of the average angular speed.

A heavy cabinet is being pulled up a ramp at constant speed. There is friction between the bottom of the cabinet and the ramp. One end of a rope is attached to a handle on the side of the cabinet, and the other end is pulled by a person standing at the top of the ramp. Which forces acting on the cabinet and the handle are distributed rather than acting at a point? Treat the cabinet and the handle as a single object. Ignore air resistance.

The force of gravity caused by the Earth The normal force caused by the ramp The force of kinetic friction caused by the ramp

Which of the following statements are true regarding torque?

The location of the axis of rotation The location where the force is applied to the object The direction and magnitude of the force

Select all of the following that are true regarding the work done from the torque.

The work is directly proportional to the magnitude of the torque. The work is directly proportional to the magnitude of the angular displacement. The work can be positive, negative, or zero.

Select all of the following combinations that are possible. Assume that there is only one torque acting on the object or system of particles.

Torque < 0 (clockwise), angular velocity > 0 (counterclockwise), angular acceleration < 0 (clockwise) Torque > 0 (counterclockwise), angular velocity < 0 (clockwise), angular acceleration > 0 (counterclockwise)

Select all of the following statements that are true regarding torque.

Torques can cause objects to rotate faster or slower. It is impossible to exert a torque without exerting a force.

A wheel is free to rotate about a line passing perpendicularly through its center. Only one torque is applied to the wheel. From your point of view (looking along the axis of rotation), the torque causes the wheel to rotate faster in the counterclockwise direction. Identify the direction of the torque exerted on the wheel.

Toward you

Match the condition on the left with the type of equilibrium on the right. Instructions

Zero net force matches Translational equilibrium Zero net torque matches Rotational equilibrium

The apparatus shown below is used to study rotational dynamics in a physics lab. The wheel is a solid uniform disk of mass M and radius R, and is free to rotate about a horizontal axle going through its center. The light rope that is wrapped around the pulley is pulled down with a force F. What is the angular acceleration of the disk?

a = 2F/MR

Which of the following objects has the greatest rotational kinetic energy? Each has mass M and radius R, and rotates with angular velocit ω.

a thin-walled cylindrical shell

You are watching the second hand of a clock go around the face smoothly without pausing or jerking. What is the direction of the angular momentum of the second hand?

away from you

Gravity and friction are examples of ____ forces.

distributed

True or false: If two forces are equal and opposite, then their associated torques are also equal and opposite.

false

When considering the force of ______ acting on an extended object, we can model the force as though it were only acting on a single point called the center of gravity.

gravity

A hoop and a solid disk of the same radius and mass are given the same initial speed at the bottom of an inclined plane. The objects roll up the incline without slipping. Which object will move the farthest distance up the incline before rolling back down the incline?

hoop

A person rides a bicycle along a straight road. From the point of view of the rider, what's the direction of the angular momentum vector of the front wheel?

left

Objects A and B having equal moments of inertia are rotating about the same axis of rotation. The rotational kinetic energy of A is one half of the rotational kinetic energy of B. Which of the following is true regarding the angular speeds of A and B?

ωA = ωB/√2

Two identical solid spheres A and B have the same mass and diameter. Both are rotating about lines passing through their centers with KA > KB. Select all of the following statements that are true.

ωA > ωB IA = IB

A constant torque of 1.00 N⋅m is applied to a wheel that starts from rest and makes one revolution in one second. What was the average power due to this torque during this time?

6.28 W

A torque of 20.0 N·m is applied to a bolt. The bolt rotates through an angle of 180 degrees. The work done in turning the bolt is

62.8 J

A model of a rectangular molecule is constructed out of particles of equal mass connected by light rods as shown. Rank the moment of inertia of the molecule about the axes A, B, and C, with the largest moment of inertia at the top and the smallest at the bottom.

A C B

If a system of particles were to keep the same angular velocity, but change the distribution of mass so that on average each particle is farther away from the axis of rotation, the rotational kinetic energy would

increase

Conservation of angular momentum applies to both the very big and the very small. When an electron drops to a lower orbit, a photon is created. If the photon has one unit of angular momentum, then the electron's angular momentum must change by _____ unit.

one

A wheel is spinning clockwise and spinning slower. Only one torque is acting on the wheel. Is the torque positive, negative, or zero?

positive

A car driving away from you applies its brakes so that it begins to slow down. What is the direction of the net torque applied to the wheels?

to the right

You are watching a car moving directly away from you. The car's tires are rolling without slipping. What is the direction of the angular momentum of the car's tires?

to your left

You are watching a car moving directly toward you. The car's tires are rolling without slipping. What is the direction of the angular momentum of the car's tires?

to your right

Pick the option below that would leave the magnitude of the angular momentum unchanged of an object with a moment of inertia I and angular speed ω.

Cut the moment of inertia in half and double the angular speed Double the moment of inertia and cut the angular speed in half

Select all of the following conditions that are true when an object is in equilibrium (both translational and rotational).

The net torque is zero. The net force is zero. The (translational) acceleration is zero.

For the seesaw in the figure, assume that both masses are the same. At what distance x does the second mass need to be placed for the seesaw to be in rotational equilibrium?

x = 1.0 m

A uniform beam of mass 10 kg has a length of 10 meters. It is oriented horizontally, that is, it is level, not tilted. Its left end is located at x = 0 m, and its right end is located at x = 10 m. A narrow support is located under the beam at x = 4 m. Where must a narrow 10 kg object be placed on top of the beam so that the beam is in rotational equilibrium?

x = 3m

Rank the following situations according to the mechanical advantage, with the largest mechanical advantage at the top and the smallest at the bottom.

1. pushes a tire jack handle down 20 cm to move a car up 4 mm2. pulls a rope down 10 m to move a piano up 1 m3. rotates a screwdriver around a circle of circum. 8 cm to rotate a screw around a ... 2 cm

Rank the following objects, each rolling without slipping down a separate ramp inclined at a different angle, according to the magnitude of the acceleration of each of their centers of mass, with the largest magnitude of the acceleration of the center of mass at the top and the smallest at the bottom.

1. solid sphere r=10cm accelerating at 10 rad/s2 2. hollow sphere r=2cm accel=40rad/s2 3. solid cylinder r=10cm accel=5 rad/s2 4. hollow cylinder r=10cm accel=4 rad/s2

A 2.00 kg hollow sphere of radius 6.00 cm starts from rest and rolls without slipping down a 10.0 degree incline. If the length of the incline is 50.0 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is

1.01 m/s

A torque of 2.00 N•m is applied to a 10.0 kg object to give it an angular acceleration. If the angular acceleration is 1.75 rad/s2, then the moment of inertia is

1.14 kg m^2

Four masses are arranged as shown. They are connected by rigid, massless rods of lengths 0.760 m and 0.500 m. What torque must be applied to cause an angular acceleration of 0.750 rad/s2 about the axis shown?

1.5 N*m

The radius of a wheel is 0.770 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.00 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. What is the torque on the wheel about its axis due to the rope?

3.85 N*m

A uniform shelf of known length and mass is suspended from two wires, and has three small statues of known masses at known locations sitting on it. Which locations would it be most helpful to pick as the axis of rotation if we want to solve for the tensions?

At the locations where wire makes contact with the shelf.

A cube rests on a flat surface. If the flat surface is horizontal, then where is the point of application of the contact forces between the cube and the flat surface?

At the middle of the bottom of the cube that is in contact with the flat surface

A box is sliding across a rough floor and is almost tipping over. Where can we consider the friction to be applied?

At the middle of the leading edge of the box

The disks shown are free to rotate about an axis passing perpendicularly through their centers. Rank them according to the magnitude of their angular acceleration, from largest at the top to smallest at the bottom.

B A D E F C

Rank the dumbbells according to the moment of inertia about an axis that passes perpendicularly through the midpoints (denoted by ×), with the largest moment of inertia at the top and the smallest at the bottom.

C A B

A turntable rotates at a constant angular velocity. Three pennies glued to the surface at three different distances from the center rotate with the turntable. Rank the following according to the moment of inertia of the pennies, with the largest moment of inertia at the top and the smallest at the bottom.

C B A

The figure shows a disk with two ants of equal mass standing at the edge. The disk is rotating freely about an axis that passes perpendicularly through its center at a constant angular speed. The two ants start walking toward the center of the disk at a constant speed. What happens to the angular speed of the disk?

It increases.

Select all of the following statements that are true regarding how to choose the axis of rotation in equilibrium problems.

The axis of rotation can be chosen arbitrarily. The best place to choose the axis is usually at the point of application of an unknown force.

Select all of the following statements that are true regarding the center of gravity of a uniform object in a uniform gravitational field.

The center of gravity is always equal to the center of mass. The force of gravity always acts at the object's center of gravity.

The radius of a wheel is 0.770 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.00 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. Which of the following equations describes rotational work?

W=τ∆θ