What is the crankshaft's angular acceleration at t = 1 s?

a) What is the crankshaft's angular acceleration at t=1s?

b) What is the crankshaft's angular acceleration at t=3s?

c) What is the crankshaft's angular acceleration at t=5s?

Solution

The angular acceleration is the derivative of the angular velocity with respect to time:

This means that, in the graph , the angular acceleraion is the slope of the curve. To solve the exercise we can simply calculate the slope of the curve in the three different points.

a) t=1 s

The initial angular velocity of this part of the motion is 50 rad/s, the final velocity is 250 rad/s, the final time is 2 s and the initial time is 0 s. The angular acceleration is

where the negative sign means it is a deceleration.

b) t= 3 s

The initial angular velocity of this part of the motion is 50 rad/s, the final velocity is still 50 rad/s, the final time is 4 s and the initial time is 2 s. The angular acceleration is

The angular acceleration in this part is zero, because the angular velocity of the object is not changing.

c) t= 5 s

The initial angular velocity of this part of the motion is 50 rad/s, the final velocity is 250 rad/s, the final time is 7 s and the initial time is 4 s. The angular acceleration is

where the positive sign means it is an acceleration.