How Do You Calculate Angular Momentum for a Particle in Motion?

[Vickie02]

Determine the angular momentum of a 60-g particle about the origin of coordinates when the particle is at x= 7.0 m, y= -6.0 m, and the velocity is v=(2.0i - 8.0k) m/s.


I don't know where to begin beyond L= I(omega)...

Any help at all would be greatly appreciated

Thanks :)

 

[Doc Al]

What's the angular momentum of a particle?

 

[ogb p]

Hi there,

Calculating angular momentum involves understanding the position, velocity, and mass of an object in motion. In this case, we have a particle with a mass of 60 grams located at (7.0, -6.0) meters with a velocity of (2.0, -8.0) meters per second.

To determine the angular momentum, we first need to calculate the linear momentum by multiplying the mass (in kilograms) by the velocity. In this case, the linear momentum would be:

p = m * v = (0.06 kg) * (2.0i - 8.0k) m/s = 0.12i - 0.48k kg*m/s

Next, we need to calculate the perpendicular distance from the origin to the particle's position. This distance is known as the moment arm and is denoted by r. In this case, the moment arm would be:

r = √(x^2 + y^2) = √(7.0^2 + (-6.0)^2) = 9.22 m

Now, we can use the formula for angular momentum:

L = r * p = (9.22 m) * (0.12i - 0.48k kg*m/s) = 1.11i - 4.42k kg*m^2/s

Therefore, the angular momentum of the particle about the origin is 1.11i - 4.42k kg*m^2/s. I hope this helps clarify the steps for calculating angular momentum. Let me know if you have any further questions. Keep up the good work!