Aferris wheel of radius r speeds up with angular acceleration α starting from rest. part a find an expression for the velocity of a rider after the ferris wheel has rotated through angle δθ.

The expression for the angular acceleration is:

where  is the variation of the angular velocity, with  being the starting velocity (which in our problem is zero), and  being the time interval. So we can write the angular velocity after an angle  as

We also know the relationship between tangential velocity, v, and the angular velocity v:

with r being the radius of the wheel. Substituting  into the previous equation, we can write an expression for v: