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 = 0.0760 s for a crankshaft with a radius of r1 = 4.25 cm to reach 1050 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

for crankshaft
w1 = 0

w2 = 1050 rpm

= 1050*2*pi/60

= 109.96 rad/s

angular acceleration of crankshaft, alfa1 = (w2 - w1)/t

= (109.96 - 0)/0.076

= 1446.78 rad/s^2

here tangential accelerations of both shafts are same.

a_tan1 = a_tan2

r1*alfa1 = r2*alfa2

==> alfa2 = alfa1*(r1/r2)

= 1446.78*(4.25/8.5)

= 723.39 rad/s^2 <<<<<<<<----------Answer

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