Angular Velocity of a wheel problem

AI Thread Summary
A wheel initially rotating at 12.5 rad/s experienced a torque for 15.7 seconds, increasing its angular velocity to 54.0 rad/s. The initial solution calculated the angle turned as 5310.9 rad, which was deemed incorrect. After clarification, the correct approach involved calculating the angular acceleration as 2.66 rad/s², leading to a more reasonable angle of 524 rad. Further discussion highlighted that using SUVAT equations could simplify the problem by omitting the need to find acceleration. The final consensus emphasized the importance of applying the right equations for angular motion.
Kallum
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The question:

A wheel was rotating at 12.5 rad/s when a torque was applied for 15.7 s. The angular velocity increased to 54.0 rad/s. What angle did the wheel turn through in that time?

My Solution:

theta = Wo*t+1/2*a*t^2
= (12.5 rad/s)(15.7)+(1/2)(41.5)(15.7)^2

therefore,

theta = 5310.9 rad.

Comment:

This answer doesn't seem right to me and I am stuck on what to do.

Thank you in advance!
 
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Welcome to PF.
It looks like you found α = 41.5. That would have been true if the specified velocity change occurred within 1 second. But it took 15.7 seconds.
 
Thank you for your responses, so I should do α = 41.5/15.7 to break it down to seconds and then use α = 2.66 rad/s as my value for acceleration?

That then gives me an answer of 524 rad. This seems more reasonable!
 
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Kallum said:
Thank you for your responses, so I should do α = 41.5/15.7 to break it down to seconds and then use α = 2.66 rad/s as my value for acceleration?

That then gives me an answer of 524 rad. This seems more reasonable!
Near enough - I get 522.
But angular movements at constant acceleration are analogous to linear ones. All the usual SUVAT equations carry over. If you remember those, for each of the five variables (initial speed, final speed, acceleration, distance, time) there is an equation that omits one and connects the other four. In this case you have initial speed, final speed and time, and you want to find distance. So there is no need to find acceleration if you pick the right equation.
 
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