Question

You want to find the moment of inertia of a complicated machine part about an axis through its center of mass. You suspend it from a wire along this axis. The wire has a torsion constant of

0.490 N⋅m/rad . You twist the part a small amount about this axis and let it go, timing 175 oscillations in 225 s .

What is its moment of inertia?

Express your answer with the appropriate units.

Answer 1

the time period

T = 225/175 = 1.28 s

angualr frequency w = 2 pi/ T = 2pi/1.28 s =4.88 rad/s

formula is

w = root k/I

I = k/ w^2

= 0.490/(4.88)^2

=0.0205 kg m^2