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 = 0.0540 s for a crankshaft with a radius of r1 = 4.75 cm to reach 1250 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

Initial angular velocity of crankshaft = 0

Final angular velocity of crankshaft = 1250 rpm = 1250*2*pi / 60 radians per second = 130.833 radians per second

time taken = 0.0540 seconds

Angular acceleration of the crankshaft = change in angular velocity / time taken = 130.833 / 0.054 = 2422.84 radians per second - squared

Linear acceleration on the belt = r1 * angular acceleration of crankshaft = 0.0475*2422.84 = 115.085 metres per second- squared

Since the belt doesn't slip, linear acceleration should be same for the camshaft as well i.e. 115.085 metres per second- squared

or,Linear acceleration on the belt = r2 * angular acceleration of larger camshaft

or, angular acceleration of larger camshaft = Linear acceleration on the belt / r2 = 115.085 / 0.095 = 1211.42 radians / second-squared

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