Aflat uniform circular disk (radius = 2.00 m, mass= 100
kg) is initially stationary. the disk is free to rotate inthe
horizontal plane about a frictionless axis perpendicular to
thecenter of the disk. a 40.0-kg person, standing 1.25 m from
theaxis, begins to run on the disk in a circular path and has
atangential speed of 2.00 m/s relative to the ground. find
theresulting angular speed (in rad/s) of the disk.

0.5 rad / s

Explanation:

Moment of inertia of the disk I₁ = 1/2 MR²

M is mass of the disc and R is radius

Putting the values in the formula

Moment of inertia of the disc  I₁  = 1/2 x 100 x 2 x 2

= 200 kgm²

Moment of inertia of man about the axis of rotation of disc

mass x( distance from axis )²

I₂  = 40 x 1.25²

= 62.5 kgm²

Let ω₁ and ω₂ be the angular speed of disc and man about the axis

ω₂ = tangential speed / radius of circular path

= 2 /1.25 rad / s

= 1.6 rad /s

ω₁ = ?

Applying conservation of angular moment ( no external torque is acting on the disc )

I₁ω₁ = I₂ω₂

200 X ω₁ = 62.5 X 1.6

ω₁ =  0.5 rad / s

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