Most gasoline engines in today\'s automobiles are belt driven. This means that t

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 = 10.3 cm to reach 672 rpm. If the belt doesn't stretch or slip, calculate the angular acceleration, 2, of the smaller camshaft which has a radius of r2 = 2.78 cm during this time period.

2 = ______ rad/s2

Explanation / Answer

angular velocity of larger camshaft is 1 = 672*2*/60 rad/s = 70.336 rad/s

Angular accularation 1 = 1/t = 70.336/0.0540 = 1302.52 rad/s2

Since there is no slipping torque of  camshaft(1) is equal to torque of  camshaft(2)

1r1 =  2r2

1302.52*10.3 /2.78=  2

2 = 4825.88 rad/s2

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