Step 1:

(a)

The angular velocity of the phonograph turntable is .

The distance from the axis of rotation is .

Convert the angular velocity from rev/min to rad/sec.

Find the angular acceleration.

Angular acceleration : ,

where is the distance from the center of axis.

is the angular velocity.

Angular acceleration of the block is .

Solution:

Angular acceleration of the block is .

Step 1:

(b)

The block exerts a force equal to the force due to friction.

Coefficient of static friction is 0.06837.

Solution:

Coefficient of static friction is 0.06837.

Step 1:

(c) 

The angular velocity of the phonograph turntable starts from rest.

Velocity reaches in 0.25 sec.

Angular velocity :

The distance from the axis of rotation is .

Find the angular acceleration.

Angular acceleration : ,

where is the distance from the center of axis.

is the angular acceleration.

Step 2:

Total angular acceleration.

Total acceleration of the block is .

Solution:

Angular acceleration of the block is .

Step 1:

(d)

The block exerts a force equal to the force due to friction.

Coefficient of static friction is 0.10399.

Solution:

Coefficient of static friction is 0.10399.