What will happen to the rotational speed?

Question

The rotational speed on a platform remains unchanged but the distance from the center of the platform is doubled. This will cause the rotational speed to

a. be quadrupled.
b. be tripled.
c. remain the same.
d. be doubled.
e. be cut in half.

Answer 1

This is an oddly worded question. If "the rotational speed...remains unchanged" as the question states, then the correct answer must be "c", mustn't it?? So I will assume that that phrase must be some kind of bizarre typo.

There are a lot of details left out of this question, so let's make the following assumptions (otherwise there's not enough info to solve the problem):
1. We're talking about a point mass that's sitting on the platform?
2. The platform itself has no mass.
3. There are no torques acting on the platform (i.e. it's just "coasting," with no engine and no friction).

In that case, the angular momentum ("L") is conserved.

L_before = L_after

If "R" is the initial distance from the center, then:

L_before = (ω_before)mR²
L_after = (ω_after)m(2R)²

So, since L_before=L_after, we have:

(ω_before)mR² = (ω_after)m(2R)²

Solve for ω_after and you get:

ω_after = ω_before / 4

So the correct answer is: "none of the above." The rotational speed drops by a factor of 4, but that was not one of the answer choices.

This was not a very well thought-out question, and you can tell your teacher I said so.

Answer 2

E.

The spinning figure skater puts out her arms, she slows down.