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 the acceleration of the cylinder have not changed.

Answer 1

Options A & C accurately describe the motion of the cylinder at the new location

Step-by-step explanation:

First of all, let's find the speed of the cylinder at the new location. If we assume that the cylinder makes one complete turn in a period

of time.

Thus, Speed v = πR/T

Therefore at the new location, since R would now be R/2, v = πR/2T it's clear the the speed has now decreased which corresponds to option A.

Now for the acceleration,

In centripetal motion, the acceleration of an object that moves in a circular path of radius with constant speed has a

magnitude given by ;

a = v²/R

From earlier, we established that both the velocity and radius of the trajectory change whenever the cylinder is moved.

Since v is now πR/2T

thus, replacing v in the acceleration equation to get;

a = (πR/2T)²/R = π²R/4T²

Comparing with the initial acceleration of a = v²/R = π²R/T², it's clear that the acceleration has decreased by a factor of 4. So the magnitude of the acceleration has decreased which corresponds to option C.

Answer 2

A and C

Step-by-step explanation:

- The cylinder will travel a smaller circumference in the same time, so its speed will decrease; since the circumference has decreased by a factor of 2, the speed will decrease by a factor of 2

- The centripetal acceleration varies with v^2/r. Where v is speed and r is the distance from cylinder and the center of turntable.

- v decreases by a factor of 2, so v^2 decreases by a factor of 4; r decreases by a factor of 2 so v^2/r decreases by a factor of 2;

- Hence, the acceleration decreases