Q: How many degrees are in 1 radian?

$$1 \ \text{rad} = 57.3^\circ = \left(\frac{180}{\pi}\right)^\circ$$

Q: A ladybug clings to the rim of a spinning wheel, spinning counterclockwise and speeding up. At the moment shown, when the bug is at the far right, what is the approximate direction of the ladybug’s total acceleration vector $$\vec{a}$$?

Up and to the left ($$\nwarrow)$$

Question 1

How many degrees are in 1 radian?

Accepted Answer

$$1 \ 	ext{rad} = 57.3^\circ = \left(\frac{180}{\pi}ight)^\circ$$

Question 2

A pocket watch and Big Ben are both keeping perfect time. Which minute hand has the larger magnitude angular velocity $$\omega$$?

Accepted Answer

Same $$\omega on $$both.

Question 3

Two cars drive around a circular track. Both take exactly 60 seconds to make one full lap. Car 1 is on the inner lane, Car 2 is on the outer lane. Which car has the larger linear velocity?

Accepted Answer

Car 2

Question 4

A small and a large wheel are connected by a belt (the belt does not slip). The small wheel turns at constant angular velocity $$\omega_S. $$How does the magnitude of the angular velocity of the large wheel $$\omega_L$$ compare to that of the small wheel?

Accepted Answer

$$\omega_S \u003e \omega_L$$

Question 5

A ladybug clings to the rim of a spinning wheel, spinning counterclockwise and speeding up. At the moment shown, when the bug is at the far right, what is the approximate direction of the ladybug’s total acceleration vector $$\vec{a}$$?

Accepted Answer

Up and to the left ($$
warrow)$$

Question 6

A small mass $$m$$ hangs from the end of a light horizontal bar which pivots about an axis through its center, but is being held stationary. The bar is then released and begins to rotate. As the bar rotates from horizontal to vertical, the magnitude of the torque on the bar:

Accepted Answer

Decreases

Question 7

For a single point mass, the moment of inertia $$I$$ about an axis a distance $$r$$ away is:

Accepted Answer

$$I = m r^2$

Question 8

Two wheels, with the same radius $$R$$ and same total mass $$M$$, rotate about their fixed axles. Wheel A is a hoop (all the mass is near the rim). Wheel B is a disk (mass is spread out uniformly). Which has the larger moment of inertia $$I$$?

Accepted Answer

The hoop

Question 9

A block and a spool are pulled on a level, frictionless surface by a string. The tension is the SAME. The masses are the same. The spool can unwind as it is pulled. Which will cross the finish line first?

Accepted Answer

The block

Question 10

A mass $$m$$ hangs from a string wrapped around a pulley of radius $$R$$ and moment of inertia $$I. $$The pivot is frictionless. As the mass accelerates downward and the pulley rotates, which has greater magnitude: the string tension $$F_T or $$the weight $$mg$$?

Accepted Answer

$$F_T \u003c mg$$

Question 11

A hoop, a solid disk, and a solid sphere, all with the same mass and the same radius, are set rolling without slipping up an incline, all with the same initial total kinetic energy. Which goes furthest up the incline?

Accepted Answer

Sphere

Question 12

A disk is spinning as shown with angular velocity $$\omega. It $$begins to slow down. While it is slowing, what is the direction of its vector angular acceleration $$\vec{\alpha}$$?

Accepted Answer

Downward ($$\downarrow)$$

Question 13

Which of the following best describes the right-hand rule for determining the direction of the angular velocity vector?

Accepted Answer

Curl your fingers in the direction of rotation; your thumb points in the direction of the angular velocity vector.

Question 14

A planet in circular orbit about the Sun is in the position shown. When the origin is located at the Sun, the vector torque on the planet due to the Sun’s gravity is:

Accepted Answer

Zero, because the force is always directed toward the Sun (the origin)

Question 15

A light rod of length $$2L$$ has two small heavy masses (each with mass $$m) $$attached at the end and the middle. The fixed axis of rotation is at the left end. What is the moment of inertia about the axis?

Accepted Answer

$$I = mL^2$ + m(2L)^2$

Question 16

A hoop, a disk, and a sphere, all with the same mass $$M$$ and radius $$R$$, are rolling along with the same speed $$v. $$Which has the most total kinetic energy?

Accepted Answer

Hoop

Question 17

If a torque is applied perpendicular to the radius vector at a distance $$r$$ from the axis, which formula gives the magnitude of the torque?

Accepted Answer

$$	au = F r \sin	heta$$

Question 18

A uniform ruler of mass $$M is $$allowed to fall freely, pivoting about one end. At the instant it is released from a horizontal position, what is the angular acceleration $$\alpha at $$the pivot?

Accepted Answer

$$\alpha = \frac{3g}{2L}$$

Question 19

Which of the following statements about rolling motion without slipping is correct?

Accepted Answer

The velocity of the center of mass $$v_{CM} is $$equal to the angular velocity $$\omega$$ times the radius $$R$$: $$v_{CM} = \omega R$$

Rotational Motion and Energy: Step-by-Step Physics Study Guide

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