Another question about circles, please help =]?

Question

Tangential velocity- is a measure of the distance an object travels along a circular path in a given amount of time. For example, if an object covers 5 seconds, then its tangential velocity is 4 pi meters per second.

A carnival ride at a carnival has seats attatched to the circumference of a larger horizontal wheel. The larger wheel has a radius of 8m and rotates at a speed of 5rpm (rotations per minute). The smaller wheel has a radius of 2 m and rotates at 20rpm.

SEE PICTURE:
http://i7.tinypic.com/2j5z2pc.jpg...

You, in the seat, feel the combined effect of both rotations. For example, suppose you are sitting at point P in the diagram. If v1 is the tangential velocity of point P, the velocity you experience will be the sum of v1 and v2. Find the maximum and mininum velocities you will experience while on the ride. (Give the magnitude only, not the direction.) Expalin your reasoning.

Answer 1

If you calculate the tangential velocities for both the big wheel (v1) and the smaller wheel with the seat (v2), you can just add them and subtract them to find the max and min velocities.

For v1, you have a wheel traveling at 5 revolutions/min. Doing some converting and knowing that 1 revolution covers 16pi meters, we have:

(5 revolutions/min)(min/60 sec)(16pi m/revolution) = 4pi/3 m/s

Likewise for v2:
(20 revolutions/min)(min/60 sec)(4pi m/revolution) = 4pi/3 m/s

Since you'll feel the combined effect of both tangential velocities, the fastest you'll feel like you're going will be 8pi/3 m/s, and the slowest you'll feel is 0 m/s.