Q: The wheel on a vehicle has a rotational inertia of $$2.0\ \text{kg} \cdot \text{m}^2. At $$the instant the wheel has a counterclockwise angular velocity of $$6.0\ \text{rad/s}$$, an average counterclockwise torque of $$5.0\ \text{N} \cdot \text{m} is $$applied, and continues for $$4.0\ \text{s}. $$What is the change in angular momentum of the wheel?

$$16\ \text{kg} \cdot \text{m}^2 / \text{s}$$

Question 1

An ice skater is spinning on frictionless ice with her arms spread outward from her body. Her initial rotational velocity is $$\omega. $$The skater then moves her arms inward toward her body. How does the final rotational velocity and rotational inertia of the skater compare to the initial values?

Accepted Answer

Rotational velocity increases; rotational inertia decreases.

Question 2

A child stands on a rotating platform at point A as shown in the figure. The platform is rotating at a constant rate of $$\omega$$ when the child begins walking along the radius of the platform to point B. Which of the following statements explains the changes in the rotational velocity of the platform?

Accepted Answer

The rotational velocity will remain the same because there are no external forces acting on the child/platform system.

Question 3

A thin hexagon shaped board is nailed through its center to the top of a horizontal table such that it is free to rotate. Four forces are applied to the board as shown in a top view of the board in the figure. What is the net torque on the board?

Accepted Answer

The net torque is zero.

Question 4

A block of mass $$m$$, and a sphere of mass $$m$$ with radius $$R$$, are propelled up inclines of the same shape with identical initial velocities $$v. $$The block moves up a frictionless incline while the sphere’s incline has enough friction so that the sphere rolls without slipping. Which of the following statements is correct concerning the velocities of the block and sphere when both have traveled a height $$h up $$their respective inclines?

Accepted Answer

Because the sphere has rotational kinetic energy, it will have a smaller velocity at $$h.$$

Question 5

A wheel rotates through $$10.0$$ radians in $$2.5$$ seconds as it is brought to rest with a constant angular acceleration. What was the initial angular velocity of the wheel before the braking began?

Accepted Answer

$$2.0\ 	ext{rad/s}$$

Question 6

A wrench has five equal forces $$V$$, $$W$$, $$X$$, $$Y$$, and $$Z$$ applied to it. Which two forces produce the same clockwise torque?

Accepted Answer

V and Z

Question 7

A square piece of plywood on a horizontal tabletop is subjected to the two horizontal forces shown above. Where should a third force of magnitude $$5\ 	ext{N} be $$applied so that the piece of plywood is in equilibrium?

Accepted Answer

At the top right corner, directed downward.

Question 8

A stunt man is jumping several cars with a motorcycle. While the rider and the motorcycle are in the air, he uses the throttle to cause the rear wheel to spin faster. What happens to the rotation of the rider-motorcycle system when the rear wheel spins faster?

Accepted Answer

Front of motorcycle rotates upward.

Question 9

A rod is made of three segments of equal length with different masses: $$m$$, $$2m$$, and $$3m. $$Will the moment of inertia of the rod be greater about the left end, greater about the right end, or the same about both ends?

Accepted Answer

Greater about the right end.

Question 10

An angler balances a fishing rod on her finger as shown. If she were to cut the rod along the dashed line, would the weight of the piece on the left-hand side be greater than, less than, or equal to the weight of the piece on the right-hand side?

Accepted Answer

Less than

Question 11

A bullet of mass $$m is $$shot at a hinged rod and hits the rod a distance $$d$$ from the hinge. The rod was initially at rest and has a moment of inertia $$I$$ about an axis through its hinge. The bullet is fired at an angle $$	heta to $$the rod, as shown in the figure. Which student’s reasoning is correct regarding the angular speed of the rod after the collision?

Accepted Answer

Ann: The angular momentum of the rod plus bullet about the hinge after the bullet is embedded is the same as the initial angular momentum of the bullet about the hinge.

Question 12

A thin hoop or ring with a radius of $$2\ 	ext{m} is $$moving so that its center of mass is initially moving at $$20\ 	ext{m/s}$$ while also rolling without slipping at $$10\ 	ext{rad/s}$$ along a horizontal surface. It rolls up an incline, coming to rest. Which energy forms must be considered in the energy bar chart for this scenario?

Accepted Answer

Translational kinetic energy, rotational kinetic energy, and gravitational potential energy.

Question 13

In each case, a 1-kg object is released from rest on a ramp at a height of $$2\ 	ext{m}$$ from the bottom. All of the spheres roll without slipping, and the blocks slide without friction. Which object will reach the horizontal surface at the bottom of the ramp with the greatest speed?

Accepted Answer

Solid sphere

Question 14

A solid sphere rolls without slipping along a track shaped as shown. It starts from rest at point $$A$$ and is moving vertically when it leaves the track at point $$B. At $$its highest point while in the air, will the sphere be (a) above, (b) below, or (c) at the same height as point $$A$$?

Accepted Answer

Below point $$A$$

Question 15

The horizontal uniform rod shown above has length $$0.60\ 	ext{m}$$ and mass $$2.0\ 	ext{kg}. $$The left end of the rod is attached to a vertical support by a frictionless hinge. The right end of the rod is supported by a cord that makes an angle of $$30^\circ$$ with the rod. A $$0.50\ 	ext{kg}$$ block is also attached to the right end of the rod. Which equation would you use to calculate the tension in the cord?

Accepted Answer

$$T = \frac{(M$$_{rod}$$g \cdot \frac{L}{2} + m$$_{block}$$g \cdot L)}{L \sin 30^\circ}$$

Question 16

A disk-shaped platform has a known rotational inertia. The platform is mounted on a fixed axle and rotates in a horizontal plane. A student wishes to determine the frictional torque exerted on the platform by the axle as the platform rotates. Which quantity must be measured to determine the frictional torque?

Accepted Answer

The angular velocity as a function of time.

Question 17

The wheel on a vehicle has a rotational inertia of $$2.0\ 	ext{kg} \cdot 	ext{m}^2. At $$the instant the wheel has a counterclockwise angular velocity of $$6.0\ 	ext{rad/s}$$, an average counterclockwise torque of $$5.0\ 	ext{N} \cdot 	ext{m} is $$applied, and continues for $$4.0\ 	ext{s}. $$What is the change in angular momentum of the wheel?

Accepted Answer

$$16\ 	ext{kg} \cdot 	ext{m}^2 / 	ext{s}$$

Question 18

The figure above shows a uniform meterstick that is set on a fulcrum at its center. A force of magnitude $$F$$ toward the bottom of the page is exerted on the meterstick at the position shown. At which of the labeled positions must an upward force of magnitude $$2F be $$exerted on the meterstick to keep the meterstick in equilibrium?

Accepted Answer

Position B

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