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The torque tau on a body about a given p...

The torque `tau` on a body about a given point is found to be equal to AxxL where A is a constant vector, and L is the angular momentum of the body about that point. From this it follows that

A

`dL//dt` is perpendiclar to `L` at all instants of time

B

the component of `L` in the direction of `A` does not change with time

C

magnitude of `L` does not change with time

D

`L` does not change with time

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`vectau=vec(dL)/(dt)`
given that `vectau=vecAxxvecL`
`implies (vec(dL))/(dt)=vecAxxvecL`
From the cross product rule `(vec(dL))/(dt)` is always perpendicular to the plane containing `vecA` and `vecL`. By the dot product definition. `vecL.vecL=vecL`
Diferentiating with respect to time, we get
`vecL(vec(dL))/(dt)+vecL(vec(dL))/(dt)=2L(vec(dL))/(dt)`
`vec(2L)(vec(dL))/(dt)=2L(dL)/(dt)`
Since `vec(dL)/(dt)` is perpendicular to `vecL`
`(dL)/(dt)=0 impliesL=`constant
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