Bubba is towing a trailer. One of the trailer\'s tires is bad. Bubba does not ha

Question

Bubba is towing a trailer. One of the trailer's tires is bad. Bubba does not have a
replacement tire, but he has an old wheel of a different size that he uses to change
out one of the trailer's wheels. One wheel has tires with a radius of 10.2 inches. The other wheel has tires with a radius of 12.7 inches. Bubba drives down the road at a constant speed of 47.5 mph.
a) Determine the rotational rate of each wheel (in radians per second).
b) Determine how many times each wheel turns after Bubba has driven a
distance of 4.25 miles.

Explanation / Answer

v = 47.5 mph = 2123.44 m/s

r1 = 10.2 inches = 0.25908 m

r2 = 12.7 inches = 0.32258 m

a) w = v/r1 = 8196.07 rad/s

w2 = v/r2 = 6582.67 rad/s

#b) theta1 = s/r1 = (6839.712/0.25908 = 26400 radians = 4203.82revolutions

heta2 = s/r2 = 6839.712/ 0.32258 = 21203.15 radians = 21203.15/6.28 = 3376.29 revolutions

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