A disk, with a radius of 0.25 m, is to be rotated like a merrygo- round through 800 rad, starting from rest, gaining angular speed at the constant rate a1 through the first 400 rad and then losing angular speed at the constant rate -a1 until it is again at rest.The magnitude of the centripetal acceleration of any portion of the disk is not to exceed 400 m/s2. (a) What is the least time required for the rotation? (b) What is the corresponding value of a1?
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.
A disk, with a radius of 0.25 m, is to be rotated like a merrygo-
round through 800 rad, starting from rest, gaining angular speed
at the constant rate a1 through the first 400 rad and then losing angular
speed at the constant rate -a1 until it is again at rest.The magnitude
of the centripetal acceleration of any portion of the disk is
not to exceed 400 m/s2. (a) What is the least time required for the rotation?
(b) What is the corresponding value of a1?
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