Physics homework help

Question

I've been stuck on this question for a while and don't know how to answer it

A 3.5 kg particle moves at a constant speed of 5 m/s around a circle of radius 8 m.

a) What is its angular momentum about the center of the circle? Answer in units of kg · m2 /s.

b) What is its moment of inertia about an axis through the center of the circle and perpendicular to the plane of the motion? Answer in units of kg · m2 .

c) What is the angular speed of the particle? Answer in units of rad/s.

Answer 1

Hi Chris F.,

Go back to your definitions of angular momentum and moment of inertia.

For angular momentm, L = r x p where L is angular momentum (pseudovector), r is the radius vector, P is the momentum vector, and x represents the cross-product of two vectors. Since the motion is circular, r and p are at right angles, and therefore you may just say 3.5 kg * 5 m/s * 8 m, directed as per the right-hand rule.

For moment of inertia, I = r^2 * m, so (8 m)^2 * 3.5 kg . Incidentally, the specification of the axis here serves only to assure that "r" has the meaning you think it does! (If the specified axis lay in the plane of motion, there wouldn't be any rotation around it, would there?

There is also L = I *ω , where ω is angular frequency (radians/s), but I imagine the previous form might be easier for you to compute?

So you should be able to compute ω, since a circle has 2π radians?

--Cheers, --Mr. d.