Angular momentum of a particle

  • #1
peachy112girl
5
0

Homework Statement


The position of a particle of mass m = 2.0kg is given at time t by the equation, r = 3t i - t2 j + 2 k, where r is measured in meters from the origin, and t is in seconds. What is the angular momentum of the particle with respect to the origin at time t = 2 s?

Homework Equations


L = Iω = (mr2)(ω)

The Attempt at a Solution


I kind of understand the general idea of the problem, I think it's just the presence of i, j, k that is confusing me.

From the radius equation, I took the derivative to get the angular velocity equation.
ω = 3 i - 2t j

From there, I calculated r(2) and ω(2).
r(2) = 6i - 4j + 2k
ω(2) = 3i - 4j

Using the equation L = Iω = mr2ω
L = (2)(6i - 4j + 2k)2(3i - 4j)

Then, I just multiplied through to get the answer. But, the numbers look way too big and I'm not too sure I did it correctly.

Any help is appreciated!
 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,915
The angular momentum is the cross product (vector product) of the momentum of the particle and its position vector. You can determine the velocity of the particle by differentiating r(t) with respect time; multiply it by mass and then calculate the cross product with the position vector.

ehild
 

Suggested for: Angular momentum of a particle

Replies
23
Views
379
Replies
13
Views
531
Replies
3
Views
244
  • Last Post
Replies
2
Views
233
Replies
8
Views
416
Replies
3
Views
321
  • Last Post
Replies
4
Views
400
  • Last Post
Replies
3
Views
571
Top