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In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it....

In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 4.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as

θ = 2.10t2 − 0.850t3

where θ is in radians and t is in seconds.

(a) Find the maximum angular speed of the roller.
rad/s

(b) What is the maximum tangential speed of a point on the rim of the roller?
m/s

(c) At what time t should the driving force be removed from the roller so that the roller does not reverse its direction of rotation?
s

(d) Through how many rotations has the roller turned between

t = 0

and the time found in part (c)?
rotations

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