physics help?

Question

A phonograph turntable is rotating at 33 1/3 rev/min. A small block is placed on the turntable 5.5 cm from the axis of rotation. The block does not slip during the rotation.

a. What is the block's acceleration?

b. What is the minimum value of the coeffiecient of static friction between the block and the turntable?

c. Suppose the turntable starts from rest and keeps accelerating uniformly so that it reaches an angular speed of 33 1/3 rev/min in 0.25 s. What is the total acceleration of the block when its angular speed is 33 1/3 rev/min?

d. In part (c) what is the minimum value of the coeffiecient of static friction required for the block to slip during the acceleration period?

Answer 1

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.

Answer 2

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.

Tangential 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 .

Answer 3

Step 1:

(d)

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

Coefficient of static friction should be greater than 0.10399 for the block to slip during accerlation period.

Solution:

Coefficient of static friction should be greater than 0.10399 for the block to slip during accerlation period.

Answer 4

Step 1:

(a)

The angular velocity of the phonograph turntable is .

The distance from the axis of rotation to box is .

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

Find the acceleration of the block.

Acceleration of the block : ,

where is the distance from the center of axis.

is the angular velocity.

Acceleration of the block is .

Solution:

Acceleration of the block is .