Suppose that you press the accelerator on your car and the engine tachometer goe

Question

Suppose that you press the accelerator on your car and the engine tachometer goes from 0 rpm to 3000 rpm in 4.0 s. We assume that the angular acceleration is constant.

a) What is the angular acceleration of the engine?

b) At a time 3.0 s after first starting to press the accelerator, what are the tangential and radial accelerations of a point on the outside of the engine crankshaft if the crankshaft has a diameter of 3.0 cm?

c) How many revolutions does the engine make during the time it’s accelerating?

Explanation / Answer

1) angular acceleration = change in angular velocity/ cange in time

= (final angular velocity- initial angular velocity ) / change in time

= (3000rpm-0)/4 = 750 rpm/s

for cnverting it into rad/s2 multiply final answer by 0.104

2)tangential acceleration = (radius of the rotation)(angular acceleration)

atan = r

atan = tangential acceleration

r = radius of the object's rotation =3/2 =1.5 cm or 0.015m

= angular acceleration, with units radians/s2

atan = 0.015*750 =11.5 m/s2

radial acceleration = w2 *r

let w3 be w at t=3s

w3 = w0 +angular acceleration*time= 0+750*3 =2250rpm =235.6 rad/s

radial acceleration = (235.6)2*0.015 =832.6 rad/s2

3) = w0*t + 0.5*/angular acceleration*time^2

time= 4/60 = 0.066 minutes

=0*4+0.5*750*(0.066)2 =1.635 Rrevolutions

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