# The angular velocity of a process control motor is (21−(1/2t^2)) rad/s

1. Sep 20, 2013

### zapzapper

1. The problem statement, all variables and given/known data
The angular velocity of a process control motor is (21−(1/2t^2)) rad/s, where t is in seconds.

1.) At what time does the motor reverse direction?

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

2. Relevant equations
angular velocity of a process control motor is (21−(1/2t^2)) rad/s

3. The attempt at a solution
For part 1 I just set the equation equal to 0 and got a time of 6.5 sec, which is correct

For part 2, I have no idea what to do. Nothing is working, so if you could help, that would be great! I have tried taking the derivative to find acceleration, which is -t, and then plugging that into θf = θi + ωi(t) + 1/2a(t^2). I set θi = 0 because I figured there would initially be no angle. I set ωi = 21 because at t=0, ω = 21. I set t= 6.5, and a=-6.5...so my equation was θf = 0 + 21(6.5s) + 1/2(-6.5)(6.5s^2), but the answer came to like -0.8125 rad? is that right? it seems odd to me...

Last edited: Sep 20, 2013
2. Sep 20, 2013

### Staff: Mentor

Hi zapzapper, Welcome to Physics Forums.

It appears that you're familiar with calculus since you mentioned taking a derivative.

Suppose this were a linear motion problem and you were given a velocity function v(t). How would you go about finding d(t) using calculus? You can apply the same method to rotational motion where velocity is represented by the variable ω and distance by θ.

3. Sep 20, 2013

### zapzapper

ok, I'll integrate the function

Last edited: Sep 20, 2013
4. Sep 20, 2013

### zapzapper

oh ok, so I just integrate the function then?, If I integrate it then I get (21t - (1/6t^3) + c), what do i do with the constant c though?

5. Sep 20, 2013

### SteamKing

Staff Emeritus
You are trying to find the total angular displacement between two known times. What happens to the constant of integration when you evaluate a definite integral?