- #1
Satvik Pandey
- 591
- 12
Homework Statement
A small ball of mass m suspended from a ceiling at a point O by a thread of length l moves along a horizontal circle with constant angular velocity ##\omega##. Find the magnitude of increment of the vector of the ball's angular momentum relative to point O picked up during half of revolution.
Homework Equations
The Attempt at a Solution
I[/B]nitial velocity of ball ##V_{i}=v\hat { j }##
Initial distance of the ball from O is (R)=##lsin\alpha\hat{i}-lcos\alpha\hat{k}##
Final velocity ##V_{f}=-V\hat{j}##
Final distance of the ball from O is ##-lsin\alpha\hat{i}-lcos\alpha\hat{k}##
Initial momentum is ##R## cross ##P##.
##L_{i}=mvLcos\alpha\hat{i}-mvlsin\alpha\hat{k}##
##L_{f}=-mvLcos\alpha\hat{i}+mvlsin\alpha\hat{k}##
##\delta L=-2mvLcos\alpha\hat{i}+2mvlsin\alpha\hat{k}##
So its magnitude is ##2mvL##
I got ##cos\alpha=\frac{g}{\omega^2l}## by writing the force equation.
Now ##v=lsin\alpha\omega##
Using this I got the answer
##2ml^{2}\omega\sqrt{1-\frac{g^{2}}{(\omega^{2}l)^2}}##
But the answer is incorrect.