Q6.13 Torque and angular momentum (H)
Write down the equation expressing the rate of change of the angular momentum of a system.
A ball is thrown from a point O. Show that the angular momentum of the ball about O is not conserved unless the ball is thrown vertically.
Show with a sketch how
- the torque on the ball, about O
- the angular momentum of the ball, about O
vary in the course of the ball’s flight.
Hint
Reveal

Hint
Don’t forget that torque (Key Point 5.15) and angular momentum (Key Point 5.16) are vectors.Solution
Reveal

Solution
The rate of change of angular momentum is given by Key Point 5.18
![\[ \vec{\tau}_{ext} = \frac{d\vec{L}}{dt} \]](mastermathpng-0.png)
If the ball is not thrown vertically, the gravitational force
The torque about O has magnitude τ=mgrsinθ=mgx, and direction perpendicular to the xy plane (into the diagram). Since x increases linearly with t, so does τ. Hence so does |