Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.

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Physics 211, Quiz 23

Question 1:
Two wheels are the same shape and mass, but
one is larger than the other:
wheel A has mass m = 2 kg, radius R(A) = 1 m
wheel B has mass m = 2 kg, radius R(B) = 2 m

Both wheels roll at the same angular speed:
**omega = 1.5 rad/s**.
Which wheel has more rotational kinetic energy? Explain.

Answer: The rotational kinetic energy depends on moment of inertia
and angular speed:
rot KE = 0.5 * I * (omega)^2
The angular speed omega is the same for both wheels, but
the moment of inertia is not. The moment of inertia depends
on mass and radius:
I = (something) * (mass) * (radius)^2
Therefore
I(A) (something) * (2 kg) * (1 m)^2 1
------ = -------------------------------- = -----
I(B) (something) * (2 kg) * (2 m)^2 4
So I(B) = 4 I(A). That means that B has 4 times as much
rotational KE as A.

Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.