A solid, uniform disk of mass M and radius a may be rotated about any axis paral

Question

A solid, uniform disk of mass M and radius a may be rotated about any axis parallel to the disk axis, at variable distances from the center of the disk. (Figure 1)

Part A

What is Icm, the moment of inertia of the disk around its center of mass? You should know this formula well.

Express your answer in terms of given variables.

Part B

If you use this disk as a pendulum bob, what is T(d), the period of the pendulum, if the axis is a distanced from the center of mass of the disk?

Express the period of the pendulum in terms of given variables.

Part C

The period of the pendulum has an extremum (a local maximum or a local minimum) for some value of dbetween zero and infinity. Is it a local maximum or a local minimum?

Explanation / Answer

a) M*a^2/2

b) For a pendulum with moment of inertia I tied at a distance d from the centre of mass, Time period = 2*pi*sqrt( I / Mgd) = 2*pi*sqrt(M*a^2/2Mgd) = 2*pi*sqrt(a^2 / 2gd)

c) Since on increasing d the time period keeps on decreasing , thus the time period has a local minima at d=a

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