A CD with a diameter of 12.0 cm starts from rest and with a constant angu acceleration of 1.00 rad/sec2 acquires an angular velocity of 5.00 rad/sec. continues rotating at 5.00 rad/sec for 15.0 seconds and then slows to a sto seconds with a constant angular deceleration. What is the total acceleratic cm from the center at the time 30. 0 seconds from the start?
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.
We know that the formula of the first equation of the angular motion is given as
where is the final angular velocity, is the initial angular velocity, and is the angular acceleration for a time t.
Here We know that the CD starts rotating from the rest and then accelerate with the constant acceleration and after some time t1 it has an angular velocity and then for a time t2 it rotates with the constant angular velocity and after that, it slows down with the angular acceleration in a time t3 it stop. let at a time t it r distance from the center at that time total acceleration of the CD is a.
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