Question

Part 1: A DVD is initially at rest so that the line PQ on the disc's surface is along the +x-axis. The disc begins to turn with a constant α = 5.0 rad/s². 

.1. At-0.40s, what is the angle between the line PQ and the +x-axis? 

A. 0.40 rad B. 0.80 rad C. 1.0 rad D. 2.0 rad  

2. How do the centripetal acceleration and tangential acceleration compare at points P and Q?

Part 2: 

3. You want to double the radius of a rotating solid sphere (I=(2/5)mR²) while keeping its kinetic energy constant. (The mass does not change.) To do this, the final angular velocity of the sphere must be 

A. 4 times its initial value. B. twice its initial value. C. the same as its initial value. D. 1/2 of its initial value. E. 1/4 of its initial value. 

4. The three objects shown here all have the same mass M and radius R. Each object is rotating about its axis of symmetry (shown in blue). All three objects have the same rotational kinetic energy. Which one is rotating fastest? 

A. thick-walled hollow cylinder B. solid cylinder C. thin-walled hollow cylinder D. two or more of these are tied for fastest 

5. A thin, very light wire is wrapped around a drum that is free to rotate. The free end of the wire is attached to a ball of mass m. The drum has the same mass m. Its radius Is R and its moment of inertia is 1 (1/2)m . As the ball falls, the drum spins. At an instant that the ball has translational kinetic energy K, the drum has rotational kinetic energy 

AK. B.2K CK/2. D. none of these

Answer 1

PART1

1. angular acceleration, a = 5 rad/s2

=> a = (angular velocity, v) /(time, t)

=> 5 = (v) / 0.4

=> v = 2 rad/s = angular position, / time

=>v = / t

=> = 2 * 0.4 = 0.80 rad

option B. 0.80 rad

2. centripetal acceleration, CA = (velocity, v)2/ radius, r

tangential acceleration, TA = radius, r * angular acceleration, a

therefore, at point P, where radius, rp is less than the radius at point Q, rq i.e., rp < rq

CA will be less at point Q and more at point P

TA will be less at point P and more at point Q

option C. Q has a smaller CA and a greater TA than P.

PART 2

3. The total kinetic energy of a rotating solid sphere is given by,

Therefore, radius of the sphere, doesn't effect the kinetic energy of the roatting sphere.

option C. the same as its initial value.

4. Using the equation for kinetic energy and substituting for moment of inertia

case 1: thick walled cylinder,

case 2: solid cylinder

case 3: thin walled cylinder

THEREFORE, the thick walled hollow cylinder rotates faster.

option A thick walled hollow cylinder

5.

transational kinetic energy,

rotational kinetic energy,

therefore, K = (1/2) R or R = 2*K

option B. 2K