What Is the Maximum Angular Momentum of a Particle Moving Past a Point?

[dinonichas]

Homework Statement

A particle moves in a straight line past a point O, as shown below. At which point is the angular momentum maximum (with respect to O)? If the minimum distance between O and the line is 2 m, and the object has a mass of 2 kg and a velocity of 3 m/s, what is the maximum angular momentum of the particle with respect to O?

Homework Equations

angular momentum is equal to:
Iω= (mr^2)mv ??

The Attempt at a Solution

0,i think,because the momentum should be 90 degree from the radius to make the angular momentum.so in this case the particle is moving in the straight line with the point O so it will be 0

 

[Phlogistonian]

angular momentum is equal to:
Iω= (mr^2)mv ??

$$\omega \neq mv$$

There is a simple formula relating angular momentum to mass, velocity, and radius vector. Find that formula in your textbook and use it.

the momentum should be 90 degree from the radius to make the angular momentum.

This is correct.

so in this case the particle is moving in the straight line with the point O so it will be 0

But this isn't. If the point O is 2 m from the line, the angular momentum (with respect to that point) can't be zero.

 

[Moetasim]

.

I would like to clarify that the concept of angular momentum is different from linear momentum. Angular momentum is a measure of the rotational motion of an object, while linear momentum is a measure of its linear motion. Therefore, the statement that the particle's momentum should be 90 degrees from the radius is not accurate in this context.

To answer the question, the maximum angular momentum of the particle with respect to O would occur when the particle is at its closest distance to O, which is 2 m. This is because angular momentum is directly proportional to the distance from the point of rotation. Using the equation for angular momentum, we can calculate the maximum angular momentum as follows:

L = Iω = mr^2ω = (2 kg)(2 m)^2(3 m/s) = 24 kg·m^2/s

Therefore, the maximum angular momentum of the particle with respect to O is 24 kg·m^2/s. It is important to note that this value may change if the mass or velocity of the particle changes, but the principle of maximum angular momentum being at the closest distance to the point of rotation remains the same.