Question

2. The previous problem requires you to use the parallel axis theorem. Is there some physical interpretation of the two terms in the parallel axis theorem? How does this physical interpretation relate to the comparison you made between the two methods of computing kinetic energy in the previous problem?

Previous:

A 250 g solid sphere and a 500 g solid sphere are connected by a massless, rigid rod that is 90 cm long, as measured between the centers of the two spheres. Both spheres have a diameter of 4 cm. The structure is rotating at 120 rpm about its center of mass. Compute the rotational kinetic energy. Do this calculation two different ways: first, treat each sphere as an extended object and use the appropriate moment of inertia; then, treat each sphere as a point particle instead. Compare the results from the two approaches.

Answer 1

about center of mass axis (for sphere)

Icm = 2 m r^2 / 5

then about the center of rod,

I = Icm + m (r + L/2)^2

I1 = (0.250 kg) ((2 0.02^2 /5) + (0.47^2)) = 0.055265 kg m^2

I2 = (0.5000 kg) ((2 0.02^2 /5) + (0.47^2)) = 0.11053 kg m^2

I = I1 + I2 = 0.165795 kg m^2

w = 120 rpm = 120 x 2pi rad / 60s = 12.56637 rad/s

KE = I w^2 /2 = 13.09065 J .....Ans

using as point particle,

I = (0.250 x 0.47^2) + (0.50 x 0.47^2) = 0.165675 kg m^2

KE = I w^2 /2 = 13.081174 J .....Ans

results are same by very extent

ratio = 13.09065 / 13.081174 = 1.000724