Will the radial acceleration be constant?

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Amith2006
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Sir,
When a torque is applied to a body undergoing uniform circular motion, will the radial acceleration be constant?
 
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Torque is defined as the time derivative of angular momentum. What do you think?
 
I think that when a torque is applied, the angular momentum increases as a result of which there a change in angular velocity and hence the radial acceleration changes. Is it right?
 
Sounds good so far. There are two ways that the angular momentum could change though, it could change its magnitude or it could rotate. You've argued what happens in the first case, but what about the second?