Angular Acceleration of a Rotating Wheel: Solving a Common Question

[mickeychief]

Can anyone help me in solving this question?

At t=0, a wheel is rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2 rad/s. Two seconds later it has turned 5 complete revolutions what is the angular acceleration of this wheel??

 

[cepheid]

The question says that the angular acceleration is constant, so why would it have changed two seconds later? Are you sure you were not asked to solve for the angular velocity?

 

[mickeychief]

I typed the question just as it was written. I am having trouble finding the formula for the solution, maybe it is written wrong??

 

[pervect]

I would say that the first step is to write the angular velocity of the wheel as a function of time. Have you tried to do this at all?

 

[HallsofIvy]

The question says that the angular acceleration is constant, so why would it have changed two seconds later? Are you sure you were not asked to solve for the angular velocity?

The problem didn't say the angular acceleration had changed. It gave the initial angular velocity and the total angle moved in 2 seconds and asked you to calculate the constant angular acceleration.

mickeychief: this is just like straight line acceleration except that you use angles instead of length:
If the accelaration is a, then the velocity after t is at+ v₀,where v₀ is the initial velocity, and the "distance" moved is (1/2)at²+ v₀t. Since you are told that v₀= 2 rad/sec and that, with t= 0, the angle ("distance") moved was
"5 complete revolutions"= 5(2pi)= 10pi radians, you have
(1/2)a(4)+ 2(2)= 10pi. Solve for a.