Question

Let R be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to a new location R/2 from the center of the turntable. Which of the following statements accurately describe the motion of the cylinder at the new location?
Check all that apply.
a. The speed of the cylinder has decreased.
b. The speed of the cylinder has increased.
c. The magnitude of the acceleration of the cylinder has decreased.
d. The magnitude of the acceleration of the cylinder has increased.
e. The speed and acceleration of the cylinder have not changed.

Answer 1

Answer:

a. The speed of the cylinder has decreased.

c. The magnitude of the acceleration of the cylinder has decreased.

Explanation:

Lets take angular speed of the turn table = ω

Linear speed at distance r from center of turn table

V=  ω r

The linear speed of the cylinder at distance R

r=R

V= ω R

When the distance become R/2 ,then new linear speed

r=R/2

V'= ω R/2

V'= ω R/2 = V/2

V'=V/2

Therefore speed of the cylinder is decreases.

The radial acceleration a

a= ω² r

When r decrease then the magnitude of the cylinder will decreases.

Therefore option a and c is correct.