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?
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!