- #1
erisedk
- 374
- 7
Homework Statement
The torque ## \vec{τ} ## on a body about a given point is found to be equal to ## \vec{A} × \vec{L} ## where ##\vec{A}## is a constant vector, and ##\vec{L}## is the angular momentum of the body about that point. From this it follows: (Multiple answers correct)
(A) ## \dfrac{d\vec{L}}{dt} ## is perpendicular to ##\vec{L}## at all instants of time
(B) the component of ##\vec{L}## in the direction of ##\vec{A}## does not change with time
(C) the magnitude of ##\vec{L}## does not change with time
(D) ##\vec{L}## does not change with time
Homework Equations
##\vec{τ} = \dfrac{d\vec{L}}{dt} ##
The Attempt at a Solution
##\vec{τ} = \dfrac{d\vec{L}}{dt} = \vec{A} × \vec{L} ##
From this equation (A) holds.
(D) will hold, i.e. only if ##\dfrac{d\vec{L}}{dt}## is 0, i.e.## \vec{A} ## is parallel to ## \vec{L} ## which has no reason to be true all the time. So, D should not be correct.
Which leaves (B) and (C). I have no idea how to prove or disprove them. Please help.