A student sits on a rotating stool holding two 4.0 kg objects. When his arms are

Question

A student sits on a rotating stool holding two 4.0 kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. 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.

(a) Find the new angular speed of the student.
rad/s

(b) Find the kinetic energy of the student system before and after the objects are pulled in.

Explanation / Answer

acc to . conservation of angular momentum, we have I1W1= I2W2 1----stands for before 2----stands for after his arms strecting (a) given : I1 =3 kg.m^2 W1=0.75 rad/s I2 = m r^2 =4 (0.6)^2 (r= 1.0m-0.4m= 0.6m when his arms pulled) = 1.44 rad/s W2=? W2= I1W1/I2 =1.5625 rad/s (b) K.E before =1/2 *I1* W1^2 K.E after = 1/2*I2* W2^2 sub. the above values .

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