The angular position of a point on the rim of a rotating wheel is given by ? = 3

Question

The angular position of a point on the rim of a rotating wheel is given by

? = 3.5 t + (-7.5)t2 + +(1.0)t3, where ? is in radians if t is given in seconds.

a) What is the angular velocity at t = 2.0 s?

b) What is the angular velociy at t = 4.0 s?

c) What is the average angular acceleration for the time interval that begins at t = 2.0 s and ends at t = 4.0 s?

d) What is the instantaneous angular acceleration at the beginning of this time interval?

e) What are the instantaneous angular accelerations at the end of this time interval?

Explanation / Answer

a) w = d(theta) / dt   = 3.5 - 14t + 3t^2

w(2) = -12.5 rad/s

b) w(4) = -4.5 rad/s

c) alpha = w(4) - w(2) / 4-2 =4 rad/s2

d) alpha = dw/dt = -14 + 6t

alpha(2) = - 2 rad/s2

e) alpha(4) = 10 rad/s2

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