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.1.The speed of the cylinder has decreased.2. The speed of the cylinder has increased.3. The magnitude of the acceleration of the cylinder has decreased.4. The magnitude of the acceleration of the cylinder has increased.5. The speed and the acceleration of the cylinder have not changed.

Answer 1

Answer:

The speed of the cylinder has decreased

Explanation:

Given data:

Distance between the center of the turn table and the cylinder = R

Distance between the center of the turn table and the cylinder when it is moved to a new point, R' = R/2

the tangential velocity in circular motion is given as:

$V=\frac{2\pi R}{T}$

where T is the time

now for R = R' = R/2

the new velocity V' comes as:

$V'=\frac{2\pi \frac{R}{2}}{T}$

or

$V'=\frac{\pi R}{T}$

thus the velocity becomes half or we can say the velocity decreases

Now, the acceleration (a) in circular motion is given as:

a = V²/R

now for

R = R' = R/2

the velocity V' = V/2

thus,

new acceleration a' comes as:

$a = \frac{(\frac{V}{2})^2}{R/2}$

or

$a'=\frac{V^2}{2R}$

thus,

the acceleration decreases by 2 times