A grandfather clock has a pendulum that consists of a thin brass disk of radius 36...

A grandfather clock has a pendulum that consists of a thin brass disk of radius 36 cm and mass 1.8 kg that is attached to a long, thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk. The pendulum should be designed so that its period is 2 s for small oscillations when the gravitational acceleration is 9.8 m/s².

(a) What should the length of the rod be?

(b) If this were a simple pendulum, what would the rod's length have to be?

[Don't forget to account for the physical size of the disk.]

(c) What would the percent error be in using the equations for a simple pendulum?

Solutions

Expert Solution

The pendulum oscillates about the pivot of the rod.If we consider dimension of the disc,it rotates about the pivot,about which its moment of inertia is calculated using parallel axis theorem. In simple pendulum-case,the disc is translating in the circular path.

genius_generous answered 1 year ago

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