Is it necessary that the direction of the angular velocity and the angular momentum are the same? If not, Why?

Asked by ashwinikumar59 | 19th Sep, 2010, 08:23: AM

Expert Answer:

No, it's not necessary.
 
Angular momentum: L = r x p = r x (mv) = m (r x v)
 
(r: position with respect tot origin, p: linear momentum, m: mass, x: cross product)
 
Also, linear velocity v = w x r
 
(w: angular velocity)
 
Therefore,            L = m [r x( w x r )].............. a vector triple product.
(solve using your knowledge of vector triple product and find the direction of the resultant L)
 
Hence, direction of L is different from that of w, in general. 
 
 

Answered by  | 19th Sep, 2010, 08:42: AM

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