In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it.The diameter of the roller is 1.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as tθ= 2.50t2 − 0.600 2t3 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)?
Angular speed, acceleration and displacement
Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.
Angular Position
Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.
In a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it.The diameter of the roller is 1.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as tθ= 2.50t2 − 0.600 2t3
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)?
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