In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 6.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as

Question:

In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 6.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as  θ = 2.70t² − 0.900t3³

where θ is in radians and t is in seconds.  

(a) Find the maximum angular speed of the roller.

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

(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?

(d) Through how many rotations has the roller turned between  t = 0 and the time found in part (c)?

a. 2.7rad/s

b. 8.1 m/s

c. 2 s

d. 3.6 rad

Explanation:

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