A wheel with an outside radius of 0.2 meters rotates about a central fixed axis.

Question

A wheel with an outside radius of 0.2 meters rotates about a central fixed axis. It's angular position is given by the relationship: ? = 3 - 2t3, where ? is measured in radians and t is in seconds. a. What is the initial angular displacement of the wheel? b. What is the angular displacement of the wheel at t = 2.0 s? c. What is the angular velocity of the wheel at t = 2.0 s? d. What is the angular acceleration of the wheel at t = 2.0 s? e. What is the centripetal acceleration at 2.0 s on the outside rim of the wheel?

Can someone help me solve this problem? I am not sure where to start.

Explanation / Answer

radius r = 0.2 m
angular position = 3-2t3

a)   initial angular displacement

1 = 3 rad

b) the angular displacement of the wheel at t = 2.0 s

2 = -13 rad

c)

the angular velocity of the wheel

= d/dt = -6t2

at t = 2 s

= -24 rad/s

d) angular acceleration = d/dt = -12 t = -24 rad/s^2

e)

centripetal acceleration a = r2 = 115.2 m/s2

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