The angular velocity of a wheel is given by w = 3t^2 + 7t.

Question

a. What is the wheel’s initial angular velocity at t = 0?
I think this should be zero but that seems too simple?

b. What is the instantaneous angular acceleration (α) at t = 2 sec?
Do I need to take the derivative of this as a function (6t + 7) and substitute 2 for t to get instantaneous acceleration?

c. What is the wheel’s angular displacement from t = 1 sec to t = 3 sec?
I need to know w to solve for angular displacement...what should w be? I thought it was zero but that doesn't seem right

Am I on the right track here?

Answer 1

a, yes simple
b. yes correct.
c. Just integrate displacement from t=1 to 3
displacement= INT w(t) dt over limits. w(t)= 3t^2 + 7t.

Answer 2

Thank you!