How to Calculate Angular Displacement in Circular Motion?

AI Thread Summary
The discussion focuses on calculating angular displacement in circular motion using the given angular velocity equation of a motor. The first part of the problem identifies that the motor reverses direction at 4.5 seconds. For the second part, participants clarify that angular displacement can be found by integrating angular velocity over time. The derived expression for displacement is 10t - (1/6)t^3, which allows for calculating the displacement at t = 4.5 seconds. The final calculation yields an angular displacement of approximately 29.81 radians.
kittycat342
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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
 
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Nidum said:
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
 
How do you get rads out of rad/s and time?
 
rpthomps said:
How do you get rads out of rad/s and time?
Multiply by time?
 
kittycat342 said:
do not know how to solve part b
Do you know how angular velocity is related to angular displacement?
 
velocity is the derivative of displacement
 
Right, and displacement is the integral of velocity. So, ...
 
kuruman said:
Right, and displacement is the integral of velocity. So, ...
displacement = 10t-1/6t^3
 
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
kuruman said:
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?
 
  • #11
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.
 
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