Question

show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the motion

Answer 1

Answer:

Given:

An object is travelling at a constant velocity.

To Prove:

Angular momentum of the body remains constant with respect to a particular point .

Proof:

Let the

• mass of the object be "m".
• Velocity be "v".

We know that we need to know the perpendicular distance connecting the concerned point with the trajectory of motion.

Angular momentum denoted by L.

L = m × v × (r⊥) = constant

For constant, v and (r⊥), we can say that the object is having constant angular momentum with respect to the point.

Please refer to the attached photo to understand better.

[Hence proved]

Answer 2

Explanation:

Our aim is to show that angular momentum always remains the same.

Let t be any time, suppose that vector v is at P.

We get momentum:

L = r x p = r x m.v

I L I = r.m.v x sin (theta)

Where theta is the smaller angle between vector r and vector v.

From the figure bellow, r.sin(theta) = OK, and it is the same perpendicular distance of O from the line of motion.

We can see that r.sin(theta) remains constant. Then I L I is constant and also vector L always remains the same in magnitude and direction.