A person with mass m p = 70 kg stands on a spinning platform disk with a radius
ID: 1448592 • Letter: A
Question
A person with mass mp = 70 kg stands on a spinning platform disk with a radius of R = 2.16 m and mass md = 188 kg. The disk is initially spinning at = 1.4 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.72 m from the center).
1.
What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk?
2.
What is the total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk?
3.
What is the final angular velocity of the disk?
4.
What is the change in the total kinetic energy of the person and disk? (A positive value means the energy increased.)
5.
What is the centripetal acceleration of the person when she is at R/3?
6.
If the person now walks back to the rim of the disk, what is the final angular speed of the disk?
Explanation / Answer
Here,
mp = 70 Kg
R = 2.16 m
md = 188 Kg
w1 = 1.4 rad/s
d = 0.72 m
a)
Total initial moment of inertia of system = 0.5 * md * R^2 + mp * R^2
Total initial moment of inertia of system = 0.5* 188 * 2.16^2 + 70 * 2.16^2
Total initial moment of inertia of system = 765.2 Kg.m^2
the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk is 765.2 Kg.m^2
b)
when the person is at 2/3 of the way
Total moment of inertia of system = 0.5 * md * R^2 + mp * R^2
Total moment of inertia of system = 0.5* 188 * 2.16^2 + 70 * 0.72^2
Total moment of inertia of system = 474.9 Kg.m^2
c)
let the final angular speed is w2
Using conservation of angular momentum
w2 * 474.9 = 1.4 * 765.2
w2 = 2.26 rad/s
the final angular speed is 2.26 rad/s
d)
change in total kinetic energy = Final kinetic energy - initial kinetic energy
change in total kinetic energy = 0.5 * 474.9 * 2.26^2 - 0.5 * 765.2 * 1.4^2
change in total kinetic energy = 462.9 J
the change in total kinetic energy is 462.9 J
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