The angular position of a point on the rim of a rotating wheel is given by ?=4.0

Question

The angular position of a point on the rim of a rotating wheel is given by ?=4.0t- 3.0t2 + t3, where ? is in radians if t is given in seconds. What is the angular velocity at t = 4.1 s? What is the angular velocity at t = 5.6 s? What is the average angular acceleration for the time interval that begins at t = 4.1 s and ends at t = 5.6 s ? What is the instantaneous angular acceleration at the beginning of this time interval? What is the instantaneous angular acceleration at the end of this time interval?

Explanation / Answer

d(?)/dt=W...........W=angular acceleration ,,,so W=3t2 - 6t + 4,,,,,,,,,a ) at t=4.1s the W is 29.83 rad/s..........b )at t=5.6s W is 64.48 rad/s.....c)average acceleration=23.1 rad/s2 d) instantaneous acceleration is 18.6rad/s at starting of tie 4.1s....e )at end of 5.6s acceleration is 27.6 rad/s2

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