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A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a mass of 150 kg, a radius of 2.0 m, and a rotational inertia of 300 kg·m2 about the axis of rotation. A 60 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 1.4 rad/s when the student starts at the rim, what is the angular speed when she is 0.70 m from the center?

Answer :

Answer: [tex]2.29\ rad/s[/tex]

Explanation:

Given

Mass of Platform M=150 kg

the radius of Platform R=2 m

Moment of inertia of Platform [tex]I=300\ kg.m^2[/tex]

Mass of student [tex]m=60\ kg[/tex]

The initial angular speed of the student is [tex]\omega _1=1.4\ rad/s[/tex]

Initially, the moment of inertia of platform and student is

[tex]I_1=\dfrac{1}{2}MR^2+mR^2\\\\I_1=300+60\times 4=540\ kg.m^2[/tex]

The final moment of inertia

[tex]I_2=\dfrac{1}{2}MR^2+mr^2\\\\I_2=300+60\times 0.7^2=329.4\ kg.m^2[/tex]

Conserving angular momentum

[tex]I_1\omega_1=I_2\omega _2\\\\540\times 1.4=329.4\times \omega_2\\\\\omega_2=\dfrac{756}{329.4}=2.29\ rad/s[/tex]

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