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A rod of length l is moving in a vertica...

A rod of length `l` is moving in a vertical plane (`x-y`) when the lowest point `A` of the rod is moved with a velocity `v`. find the a angular velocity of the rod and `b` velocity of the end `B`.

Text Solution

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Since the rod is rigid, thecomponents of `v_(A)` and `v_(B)` along the rod are equal. Thus,

`v_(B)costheta=v_(A)sintheta=vsintheta`
`implies v_(B)=vtantheta`…………i
Then `omega_(BA)=v_(BA)/l=(v_(BA_(_|_)))/l`
`=(|v_(A)costheta-(-v_(B)sintheta)|)/l`
`(v_(A)costheta+v_(B)sintheta)/l`............ii
Using eqn i and ii `omega_(BA)=v/(lcostheta)`
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