Question

A student sits on a rotating stool holding two 2.7-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 · m^{2}

and is assumed to be constant. The student then pulls in the objects horizontally to 0.43 m from the rotation axis.

(a) Find the new angular speed of the student.

rad/s

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

before | J |

after | J |

Answer #1

Page no. 1

Given information,

i) mass of objects = m = 2.7 kg

ii) distance of objhect before objects are pulled in =
r_{1} = 1.0 m

iii) angular speed before objects are pulled in w_{1} =
0075 rad / s

iv) Moment of inertia of the student and stool is Is = 3 kg .
m^{2}

v) Distance of object after objects are pulled in =
r_{2} = 0.43 m

To find,

i) angular speed after objects are pulled in

ii) Kinetic energy of the student before and after the objects are pulled in.

Here , no external torque is acting on the body

Hence angular momentum L = Iw is conserved.

Initial moment of inertia of the system is

I_{i} = I_{s} + 2 mr_{1}^{2}
this term is added because student is holding two objects of 2.7 kg
masds at certain distance ( r_{1} = 10 m )

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