Two wheels having the same radius and mass rotate at the same angular velocity. One wheel...
Two wheels having the same radius and mass rotate at the same angular velocity. One wheel is made with spokes so nearly all the mass is at the rim, as shown. The other is a solid disk. How do their rotational kinetic energies compare?
Homework Answers
Wheel 1 is made with spokes and wheel 2 is a solid disk.
Mass of wheel 1 = Mass of wheel 2 = M
Radius of wheel 1 = Radius of wheel 2 = R
Angular velocity of wheel 1 = Angular velocity of wheel 2 =
Moment of inertia of wheel 1 = I1
I1 = MR2
Moment of inertia of wheel 2 = I2
I2 = MR2/2
Rotational kinetic energy of wheel 1 = KE1
KE1 = I12
KE1 = MR22
Rotational energy of wheel 2 = KE2
KE2 = I22
KE2 = MR22/2
Therefore,
KE1 = 2KE2
Rotational kinetic energy of the wheel made with spokes is double that of the wheel made of a solid disk.
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