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Unit 1. Newtonian Mechanics
V. Rotational motion

1.A uniform sphere rolls down a smooth incline of angle θ to the horizontal. A student releases the ball from rest, and records the distance d the ball rolls down the plane as a function of time t. The student finds that a graph of d on the vertical axis vs. t2 on the horizontal axis makes a straight line. Which of the following should be the slope of this line in terms of the gravitational acceleration g?
(5/14)g·sin θ
(1/2)g·sin θ
(5/7)g·sin θ
g·sin θ
(1/2)g
2.The planar objects pictured above all have total mass M. Choices (A) and (B) are solid disks. Choices (C) and (D) consist of discrete masses connected by thin, light rods. Choice (E) is a hollow disk. Which has the largest moment of inertia when pivoted at the center and rotated about an axis that comes straight out of the page?
A
B
C
D
E
3.A bar of length L is rotated about the y axis, as shown above. Its moment of inertia is I. If the bar’s length is doubled, and it is still rotated about its center, what is its new moment of inertia?
(1/12) I
(1/3) I
4 I
2 I
12 I
4.The uniform rectangular block of mass M, shown above, has dimensions L x ½L. The block sits on a rough surface. A force F is applied at the location shown above. As a result of this force, the block does not slide, but rather tilts forward about point A. What is the net torque applied to the block just as it begins to tilt?
5.A typical bicycle might have 65 cm diameter tires and average a speed of 20 m/s. Which of the following is a reasonable estimate of the angular speed of the wheels?
0.02 rad/s
20 rad/s
120 rad/s
600 rad/s
60 rad/s
6.A person stands on a frictionless rotating platform. She initially keeps her arms outstretched. As she brings her arms in toward her body, which of the following quantities increases?
Her angular momentum
The linear momentum of her center of mass
Her angular velocity
Her moment of inertia
Her mass
7.The pendulum shown above is released from rest at point P. Consider point Q, at the bottom of the bob’s swing. Which of the following is correct about the bob’s tangential and centripetal acceleration at point Q?
centripetal acceleration = nonzero, tangential acceleration = zero
centripetal acceleration = zero, tangential acceleration = nonzero
centripetal acceleration = nonzero, tangential acceleration = nonzero
centripetal acceleration = zero, tangential acceleration = zero
centripetal acceleration = nonzero, tangential acceleration = either zero or nonzero, depending on the bob's speed
8.The uniform rod of length L and mass M, shown above, is pivoted on its left-hand edge. Its moment of inertia about this axis is . The rod is released from rest. When it reaches a vertical position, what is the linear speed of the rod’s center of mass?
9.Two blocks are connected by a light string over a massive pulley, as shown above. The tension in the right-hand string is T2; the tension in the left-hand string is T1. The right-hand mass m2 is greater than the left-hand mass m1. Which of the following shows a correct relationship among the tensions and weights?
m2g = T2 > T1
m2g = T2 = T1
m2g > T2 > T1
m1g = T2 = T1
m1g = T2 > T1
10.A Ferris wheel is speeding up in the clockwise direction. Which of the following could be the direction of the acceleration of the cart that is circled in the diagram above?
A
B
C
D
E