Question

A CD spins at a constant angular velocity of 4.0 revolutions per second clockwise. Which of the statements about the CD is true?
A. No net torque acts on it at all.
B. A net torque acts on it clockwise to keep it moving.
C. A net torque acts on it counterclockwise to keep it moving.

**Not sure! Thank you:)

Answer 1

If a torque is applied, the movement should be in the same direction. If there is a rotation, or some circular motion, a torque has to be applied, I guesss. So, yeah

Answer 2

movement should be in the same direction as the torque*

Answer 3

ohh so the net torque would be acting on it clockwise?

Answer 4

We need to relate torque to velocity somehow, so let's use definitions since they are all we have: \[\Large \bar \tau = \bar r \times \bar F\] We know force is mass times acceleration, so we plug that in: \[\Large \bar F = m \bar a\] and what is acceleration? It's a change of velocity and here it says constant velocity doesn't it?

Answer 5

I would believe so. I feel unsure for some reason, lol.

Answer 6

yes:) @Kainui

Answer 7

Another way you should think of stuff is when they say "constant velocity" or constant anything is to write down that its derivative is 0\[\Large \frac{d \omega}{dt}=0\] If you don't know what derivatives are, don't worry, just think about whatever value is the changing version of that. So if they say position is constant, velocity is 0. If velocity is constant, acceleration is 0. So alternatively just as good write: \[\Large \alpha = 0\] and now you just have to relate torque to angular acceleration. =P

Answer 8

ohh okay:)

Answer 9

wait so it would be moving clockwise with torque based on those explanations?

Answer 10

Nooooo

Answer 11

yes that's what i mean :)

Answer 12

wait @Kainui it's not?

Answer 13

Since torque depends on force and force depends on acceleration, since there is 0 acceleration (constant velocity) then that means there must also be 0 torque! \[\Large \tau = r \times F = r \times (m a) \]

Answer 14

oh so it's no torque is used? not torque moving clockwise?

Answer 15

Well I should probably be more specific in that the net torque is 0. It's the only way you can move at a constant velocity. In reality there will be a torque applied to spin it, but there will be resistance to torque from friction. But since you have achieved a constant velocity, then they have cancelled each other out.

Answer 16

ahh okay:) so no net torque!

Answer 17

But it's always accelerating since it's circular motion, right?

Answer 18

yes circular motion! wait so it would keep moving?

Answer 19

Oh, not angular velocity. I got you now, I think.

Answer 20

There are three types of acceleration that should try to clear up in your mind, and those are tangential, centripetal, and angular.

Answer 21

ahh okay:) and this is centripetal right?

Answer 22

I thought torque in a real system could never be 0

Answer 23

Technically we're talking about all of them right now haha. But more specifically since the problem has given you angular velocity we are "looking" at acceleration as being angular. That would be your best interpretation here. But they are all really one.

Answer 24

ohh okay:) thank you guys:)

Answer 25

Wait wait, no kai is right, since the `angular velocity` is `constant`, then the net torque is 0.

Answer 26

haha ahh okie:) thanks for explaining all this!! :D

Answer 27

Well a more direct formula is: \[\Large \tau = m r^2 \alpha\]

Answer 28

ohh okie:)

Answer 29

Since we know alpha = 0, then tau = 0.

Answer 30

Bingo

Answer 31

haha yes bingo:)

Answer 32

But of course you shouldn't ever really memorize things like that unless it's by pure accident. Remember a few formulas and then chain them together when you need to to get the results you need. Although even this is a questionable approach.

In your mind you should try to imagine these scenarios and imagine what a torque really is and be able to clearly less that there can't possibly be a net torque on a constant velocity object since a torque is really a change in angular momentum. Since the mass and velocity aren't changing, there can be no torque!

Answer 33

ahh okay will do! makes sense to me now, thank you so much!! :)