## anonymous 4 years ago in circular motion angular mometum is cont. or angular velocity is constant??

1. JamesJ

In uniform circular motion, is angular momentum a constant, is that what you're asking? The answer is it depends. Angular momentum, L, is by definition $L = r \times p = r \times mv$ This will be constant if you're measuring angular momentum from the center of the circle of motion. But for all other points, it is not.

2. anonymous

and angular velocity differ at every point rit

3. JamesJ

correct, because the vector r changes with the point from which you're measuring it.

4. anonymous

i m tired to xplain this thing to arvind he is not listening.. and even accepting !!! well thnx for help he believes u thats y i ask u too ans..

5. AravindG

but if r is same ??

6. anonymous

now u agree arvind

7. AravindG

is angular velocity same?

8. anonymous

but do u know its linear velocity??

9. JamesJ

To be explicit, suppose a body of mass m = 1 kg is moving in uniform circular motion in the xy-plane about the origin at a distance R at an angular velocity $$\omega$$. Then the displacement vector r(t) is given by $r(t) = R(\cos \omega t, \sin \omega t, 0)$ The velocity is given by differentiating, $v(t) = R \omega (- \sin \omega t, \cos \omega t, 0)$ The angular velocity of as measured from the origin is $L = r \times mv = r \times v$ $= R^2\omega (0, 0, \cos^2 \omega t + \sin^2 \omega t)$ $= R^2\omega (0,0,1)$ This is constant.

10. AravindG

so angular velocity is constant??

11. anonymous

yea by thi it is concluding linear velocity is const. means angular velocity is const. if r is same

12. JamesJ

Provided the motion is uniform (i.e., constant angular velocity omega) _and_ we are measuring angular velocity from the origin, the center of the motion. As an exercise, calculate L if we measure r from an arbitrary point (a,b). You will see it is not a constant.

13. anonymous

wat abu my sentence i wrote i become confuse

14. JamesJ

Or even an arbitrary point (a,b,c) where this is not = (0,0,0)

15. anonymous

by ur exmple

16. JamesJ

In uniform circular motion, UCM, the vector r is not a constant, nor is the vector v. What is constant is the angular speed $$\omega$$.

17. AravindG

oh cnfusing

18. anonymous

ok... got it got it thnx i think brent need ur help luk at his

19. JamesJ

The _magnitude_ of r and v are constant. But the vectors themselves are not constant, as written above.

20. JamesJ

The magnitude of r, $$|r| = R$$, a constant. The magnitude of v, $$|v| = R\omega$$, is also a constant.

21. AravindG

and w is const for UCM??

22. JamesJ

Yes, by definition.

23. anonymous

i dont have any more medals so that i can give u :(

24. JamesJ

If $$\omega$$ was not constant, then the object would not be moving around at the same rate for all $$t$$. But we define UCM to to be the angular velocity $$\omega$$ is constant.