Hi Lynn,
When I looked at your numbers my immediate reaction was that they can't be correct. For example you say that pulley A spins at 0.08 rads/min. There are 2 radians in one revolution and is approximately 3 so there are approximately 6 rads/revolution.
(6 rads/revolution) / (0.08 rads/min) = 75 min/revolution
When the belt is moving at 32 miles per hour the pulley can't take 75 minutes to make one revolution.
The belt is moving at 32 mph. There are 5280 feet in a mile, 12 inches in a foot and 60 minutes in an hour so
32 miles/hour = ^{(32 x 5280 x 12)}/_{60} = 33792 inches/minute
Pulley A has a radius of 7 inches and hence a circumference of 14 inches. One revolution of the pulley is 2 radians and hence on the circumference of the pulley there are 7 inches/radian.
Thus the pulley is spinning at the rate of
^{33792}/_{7} = 4827 radians/minute.
Penny
