**Problem : **
A disk of mass 2 kg and radius .5 m is hung from a wire, then rotated a small
angle such that it engages in torsional oscillation. The period of oscillation
is measured at 2 seconds. Given that the moment of inertia of a disk is given by
*I* = , find the torsional constant, *κ*, of the wire.

Solving for *κ*
,

**Problem : **
The disk from problem 1 is replaced with an object of unknown mass and shape,
and rotated such that it engages in torsional oscillation. The period of
oscillation is observed to be 4 seconds. Find the moment of inertia of the
object.

Solving for I,

**Problem : **
A pendulum of length *L* is displaced an angle *θ*, and is observed to have a
period of 4 seconds. The string is then cut in half, and displaced to the same
angle *θ*. How does this effect the period of oscillation?

**Problem : **
A pendulum is commonly used to calculate the acceleration due to gravity at
various points around the earth. Often areas with low acceleration indicate a
cavity in the earth in the area, many times filled with petroleum. An oil
prospector uses a pendulum of length 1 meter, and observes it to oscillate with
a period of 2 seconds. What is the acceleration due to gravity at this point?

Solving for g:

g | = | ||

= | = 9.87 m/s^{2} |

This value indicates a region of high density near the point of measurement- probably not a good place to drill for oil.

**Problem : **
What is the angular velocity of a particle moving in uniform circular motion
that has the same period as a mass of 2 kg on a spring with constant 8 N/m?

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