Physics

Problem

Two identical wheels

A

and

B

begin to rotate about parallel fixed axes at the same instant. Wheel

A

starts from rest and has a constant angular acceleration of

3.0\,\text{rad\,s}^{-2}

. Wheel

B

starts with an initial angular speed of

12\,\text{rad\,s}^{-1}

but is retarding uniformly with an angular deceleration of

1.0\,\text{rad\,s}^{-2}

. a. (i) Write the expression for the angular displacement of each wheel after a time

t

. b. (ii) Determine the time after the start when both wheels have turned through the same angle. c. (iii) Calculate this common angular displacement. d. (iv) Compute the angular speed of each wheel at that instant and state which wheel is rotating faster.

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