How to Calculate Angular Displacement in Circular Motion?

[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

 

[kittycat342]

That expression could be interpreted in different ways . Could you please write it out more clearly so that we are certain what is meant ?

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

 

[rpthomps]

How do you get rads out of rad/s and time?

 

[kittycat342]

How do you get rads out of rad/s and time?

Multiply by time?

 

[kuruman]

do not know how to solve part b

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

 

[kittycat342]

velocity is the derivative of displacement

 

[kuruman]

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

 

[kittycat342]

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

displacement = 10t-1/6t^3

 

[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?

 

[kittycat342]

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?

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

 

[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.