A body rotating at 20 rad/s is acted upon by a constant torque providing it a deceleration of 2 rad/s 2 . At what time will the body have kinetic energy same as the initial value if the torque continues to act?

Question

Philoid · Accepted Answer

The time taken is 20 sec

Given

The body rotates at a speed of 20 rad/sec with a deceleration of 2 rad/sec2.

Formula Used

The formula used in this problem is the simple angular kinematics which states that the difference between the final and initial angular velocity is equal to the product of angular acceleration and time.

where

The initial velocity of the motion is denoted by ω and the final velocity is denoted by ω₀

Explanation

The initial velocity is equal to the value of angular acceleration making the value of velocity and acceleration as 20 rad/sec; 20 rad/sec². Therefore, the initial velocity is equivalent to

Now calculating the time taken for the torque to be equal to the kinetic energy is

A body rotating at 20 rad/s is acted upon by a constant torque providing it a deceleration of 2 rad/s2. At what time will the body have kinetic energy same as the initial value if the torque continues to act?

A body rotating at 20 rad/s is acted upon by a constant torque providing it a deceleration of 2 rad/s². At what time will the body have kinetic energy same as the initial value if the torque continues to act?