# Circular Motion Problem

1. Sep 18, 2016

### kittycat342

[moderator's note: Thread moved from forum General Physics, so no template shown]

The angular velocity of a process control motor is (10−1/2t^2) rad/s, where t is in seconds.

a. At what time does the motor reverse direction?
I got 4.5 s which is correct

b. Through what angle does the motor turn between t =0 s and the instant at which it reverses direction?

I do not know how to solve part b

2. Sep 18, 2016

### kittycat342

That was all that I was given. I am looking for the Delta theta

3. Sep 18, 2016

### rpthomps

4. Sep 18, 2016

### kittycat342

Multiply by time?

5. Sep 18, 2016

### kuruman

Do you know how angular velocity is related to angular displacement?

6. Sep 18, 2016

### kittycat342

velocity is the derivative of displacement

7. Sep 18, 2016

### kuruman

Right, and displacement is the integral of velocity. So, ...

8. Sep 18, 2016

### kittycat342

displacement = 10t-1/6t^3

9. Sep 18, 2016

### kuruman

Right. I would write this as, displacement = 10t-(1/6) t^3 otherwise you might think that t^3 is multiplied by 6. Now reread question b. Can you answer it?

10. Sep 18, 2016

### kittycat342

Can I just plug in time? so 45 - (1/6)*4.5^3 = 29.81?

11. Sep 18, 2016

### kuruman

Sure. You derived an expression that gives you the angular displacement at any time t and you are looking for the angular displacement at the specific time t = 4.5 s.