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 = 4.75 cm to reach 1450 rpm. If the belt doesn't stretch or slip, calculate the angular acceleration, 2, of the larger camshaft, which has a radius of r2 = 9.50 cm, during this time period.

Explanation / Answer

Linear velocity of two belts is equal

Thus

v1 = v2

1r1 = 2r2

2 = (r1/r2)1 = (4.75/9.50)1450 = 925 rpm = 96.87 rad/s

2 = (2 – 1)/t = (96.87 – 0)/0.0320 = 3027.2 rad/s^2

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