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A uniform rod of length L and mass M is ...

A uniform rod of length `L` and mass `M` is pivoted freely at one end and placed in vertical position.
a. What is angular acceleration of the rod when it is at an angle `theta` with the vertical?
b. What is the tangential linear acceleration of the free end when the rod is horizontal?

A

`gsintheta`

B

`g/Lsintheta`

C

`(3g)/(2L) sintheta`

D

`6gLsintheta`

Text Solution

Verified by Experts

The correct Answer is:
C
The moment of inertia of the uniform rod about an axis through one end and perpendicular to length is
`I=(ML^(2))/3`
Torque `(t=Ia)` acting on the gravity of the rod is given by
`tau=Mg [L/2sintheta]`
or `(ML^(2))/3alpha=Mg L/2 sintheta`
`alpha=(3g)/(2L)sintheta`
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