Rotating Wheel The rotational position of a point on the rim of a rotating wheel

Question

Rotating Wheel The rotational position of a point on the rim of a rotating wheel is given by ? = 7.0t - 3.0t2 + t3, where ? is in radians and t is given in seconds.

Explanation / Answer

a)w = d(teta)/dt = 7-6t+3t^2 at t= 6, w = 7-36+108 = 7+72 = 79 rad/sec b)t = 8 => w = 7-48+(64*3) = 151 rad/s d)the instantaneous rotational acceleration at time t = dw/dt = -6+6t the instantaneous rotational acceleration at t = 6 = -6+36 = 30 rad/s^2 e)the instantaneous rotational acceleration at t = 8 is -6+48 = 42 rad/s^2 c)the average rotational acceleration for the time interval that begins at t = 6 s and ends at t = 8.0 s = (42+30)/2 = 72/2 = 36 rad/s^2

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