Angular momentum about an origin (O,O,O)

In summary, the problem is asking to calculate the angular momentum of a particle of mass m moving along two different trajectories, (a) and (b), with respect to the origin O=(0,0,0). The relevant equations are L = r x p and L = mvr. The student is unsure how to proceed and is seeking assistance.
  • #1
Tui
15
0

Homework Statement



Calculate the angular momentum about the origin O=(0,0,0) of a particle of mass m moving
along the following two trajectories:

(a) x(t)=vt y(t)=b z(t)=0
(b) x(t)=Rcos(wt) y(t)= Rsin(wt) z(t)=vt

Homework Equations


L = r x p
L = mvr


The Attempt at a Solution



I wasn't really sure to begin. I thought maybe I could do
L= m(vxr)
L=m ( (mv,0,0)x(vt...) Not sure what the vector equation for P is and also not sure what to do about the mass

Please help!
 
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  • #2
Any help is GREATLY appreciated D: Kinda urgent
 

Related to Angular momentum about an origin (O,O,O)

1. What is angular momentum about an origin?

Angular momentum about an origin, also known as orbital angular momentum, is a measure of the rotational energy of an object around a specific point or origin. It takes into account the mass, velocity, and distance from the origin.

2. How is angular momentum about an origin calculated?

Angular momentum about an origin is calculated by multiplying the mass of the object by its linear velocity and its distance from the origin, and then multiplying that by the sine of the angle between the velocity and the distance vectors.

3. What is the relationship between angular momentum and angular velocity?

Angular momentum and angular velocity are closely related, as angular momentum is the product of an object's moment of inertia and its angular velocity. An increase in either one will result in an increase in angular momentum.

4. What are some real-world applications of angular momentum about an origin?

Angular momentum about an origin has many real-world applications, such as in the spinning of tops and gyroscopes, the rotation of planets and stars, and the motion of satellites and spacecraft.

5. Can angular momentum about an origin be conserved?

Yes, angular momentum about an origin can be conserved in a closed system where there are no external torques acting on the system. This is known as the law of conservation of angular momentum.

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