Mary is an avid game show fan and one of the contestants on a popular game show. She spins the wheel, and after 5.5 revolutions, the wheel comes to rest on a space that has a $1500 value prize. If the initial angular speed of the wheel is 3.15 rad/s, find the angle through which the wheel has turned when the angular speed reaches 1.80 rad/s

The angle is 23.2 radians, equivalent to 3.69 revolutions.

Explanation:

First, we need to find the angular acceleration of the wheel. This can be done using one of the kinematic formulas:

Since the final angular velocity is zero after 5.5 revolutions (equivalent to 11π radians) we have that:

Now, using the same equation, we can solve for the requested angle:

Finally, it means that the angle through which the wheel has turned when the angular speed reaches 1.80 rad/s is 23.2 radians, equivalent to 3.69 revolutions.

real, smaller and upside-down.   so the answer should be b.