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Physics: Conservation of Angular Momentum?
A flat uniform circular disk (radius = 3.784 m, mass = 240 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 50.0-kg person, standing 0.684 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 1.70 m/s relative to the ground. Find the resulting angular speed (in rad/s) of the disk.
I got 0.0495 rad/s, but that's wrong.
- az_lenderLv 71 month ago
Moment of inertia of the disk is (1/2)(240 kg)(3.784 m)^2.
Moment of inertia of the man = (50.0 kg)(0.684 m)^2.
His angular velocity is (1.70 m/s)/(0.684 m/rad) = 2.485 rad/s.
His angular momentum is (2.485*50.0*0.684^2) kg*m^2/s.
So the angular velocity of the disk will be
(2.485*50.0*0.684^2*2/(240*3.784^2)) radians per sec.
I get 0.0334 rad/second.
- AshLv 71 month ago
The man is running at a distance from 0.684 m . So that will be the radius, since tangential speed is at that radius too.
ω = v/r = (1.70 m/s)/(0.684 m) = 2.49 rad/s