Astudent sits on a rotating stool holding two 1 kg objects. when his arms are extended horizontally, the objects are 1 m from the axis of rotation, and he rotates with angular speed of 0.76 rad/sec. calculate the final angular speed of the student.

The angular speed of the student is 1.144 rad/s.

Explanation:

Given that,

Mass of two objects = 1 kg

Distance = 1 m

Angular speed = 0.76 rad/s

Suppose The moment of inertia of the student plus stool is 3.0 kg-m² and is assumed to be constant. The student then pulls the objects horizontally to 0.40 m from the rotation axis.

We need to calculate the initial moment of inertia of the student & stool plus the two masses:

Using formula of moment of inertia

Put the value into the formula

We need to calculate the the final moment of inertia of the student & stool plus the two masses

Using formula of moment of inertia

Put the value into the formula

We need to calculate the angular speed

Using conservation of momentum

Put the value into the formula

Hence,The angular speed of the student is 1.144 rad/s.

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