In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 9.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as 0 - 2.90t? - 0.900t where 0 is in radians and t is in seconds. (a) Find the maximum angular speed of the roller. 3.11 v rad/s (b) What is the maximum tangential speed of a point on the rim of the roller? 14.016 v 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? 2.148 (d) Through how many rotations has the roller turned between t = 0 and the time found in part (c)? 4.46

Question

Need help on part d please.

In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 9.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as
0 - 2.90t? - 0.900t
where 0 is in radians and t is in seconds.
(a) Find the maximum angular speed of the roller.
3.11
v rad/s
(b) What is the maximum tangential speed of a point on the rim of the roller?
14.016
v 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?
2.148
(d) Through how many rotations has the roller turned between t = 0 and the time found in part (c)?
4.46
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Transcribed Image Text

In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 9.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as 0 - 2.90t? - 0.900t where 0 is in radians and t is in seconds. (a) Find the maximum angular speed of the roller. 3.11 v rad/s (b) What is the maximum tangential speed of a point on the rim of the roller? 14.016 v 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? 2.148 (d) Through how many rotations has the roller turned between t = 0 and the time found in part (c)? 4.46

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