An object starts from rest and accelerates at a rate of 2 rad/s2 until it reaches...

An object starts from rest and accelerates at a rate of 2 rad/s² until it reaches an angular speed of 23 rad/s. The object then accelerates at a constant rate of a rad/s² until it stops. If the angular displacement is 193 rad, what is the angular acceleration a (in rad/s²)?

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Expert Solution

The problem can be solved by using the rotational equations of motion. Initially the object was at rest. Therefore, the initial angular speed = 0rad/s. In the first part, the angular acceleration of the object is = 2 rads^2 and reaches a final angular velocity of = 23rad/s. The angular displacement in this part of motion can be found by,

So the angular displacement of the object in the first part of motion is 132.25rad.

Given the total angular displacemet in the entire motion, = 193rad. So the angular displacement in the second part of the motion is,

In the second part, the initial angular speed is = 23rad/s and eventually it is co,ing to stop. So the final angular speed in the second part is = 0rad/s. The angular acceleration in this part is a rad/s^2. It is given by,

So the scond part, the angular acceleration of the object is 4.35rad/s^2. Therefore the angular acceleration a is 4.35rad/s^2.

genius_generous answered 1 year ago

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