Question

in circular motion angular mometum is cont. or angular velocity is constant??

Answer 1

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.

Answer 2

and angular velocity differ at every point rit

Answer 3

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

Answer 4

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..

Answer 5

but if r is same ??

Answer 6

now u agree arvind

Answer 7

is angular velocity same?

Answer 8

but do u know its linear velocity??

Answer 9

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.

Answer 10

so angular velocity is constant??

Answer 11

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

Answer 12

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.

Answer 13

wat abu my sentence i wrote i become confuse

Answer 14

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

Answer 15

by ur exmple

Answer 16

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

Answer 17

oh cnfusing

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

and w is const for UCM??

Answer 22

Yes, by definition.

Answer 23

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

Answer 24

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.