Most gasoline engines in today\\\'s automobiles are belt driven. This means that

Question

Most gasoline engines in today's automobiles are belt driven. This means that the crankshaft, a rod which rotates and drives the pistons, is timed to the camshaft, the mechanism which actuates the valves, by means of a belt. Starting from rest, assume it takes t = 0.0320 s for a crankshaft with a radius of r1 = 4.25 cm to reach 1550 rpm. If the belt doesn't stretch or slip, calculate the angular acceleration, 2, of the larger camshaft, which has a radius of r2 = 8.50 cm, during this time period.

Explanation / Answer

Using angular momentum conservation:

m*w1*r1 = m*w2*r2

w2 = w1*(r1/r2)

w1 = 1550 rpm = 162.31 rad/sec

r1 = 4.25 cm = 0.0425 m

r2 = 8.5 cm = 0.085 m

wf = 162.31*(0.0425/0.085) = 81.155 rad/sec

alpha2 = angular acceleration

alpha2 = w2/t = 81.155/0.032 = 2536.09 rad/sec^2

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