Finding angular momentum from mv and radius in a magnetic field

[eku_girl83]

Here's my problem:

A particle with charge 4.5E-19 C travels in a circular orbit with radius .465 m due to the force exerted on it by a magnetic field with magnitude 1.7 T and perpendicular to the orbit.

a) What is the magnitude of the momentum p of the particle?
I used the equation R=(mv)/(qB) and calculated mv (linear momentum) to be 3.6E-19 kg*m/s.

b) What is the magnitude of the angular momentum L of the particle?
Herein lies the rub! Angular momentum = v/R = qB/m
I don't know velocity or mass independently, only their product (mv). So how do I calculate angular momentum?

Thanks for any help!

 

[gnome]

angular speed: ω = v/r

angular momentum: L = r x p

Since your particle is moving in a circle, it's linear momentum vector p is always perpendicular to the position vector (radius) r so the angular momentum is simply the product:
L = rp = rmv

 

[M98Ranger]

Your approach to finding the linear momentum of the particle is correct. To find the angular momentum, you can use the formula L = mvr, where m is the mass of the particle, v is its velocity, and r is the radius of the circular orbit. Since you already know the value of mv, you can rearrange the equation to solve for angular momentum: L = mv*r.

In this case, the value of mv you calculated in part a) can be used, and the radius of the orbit is given as 0.465 m. Therefore, the angular momentum of the particle is L = (3.6E-19 kg*m/s)*(0.465 m) = 1.674E-19 kg*m^2/s.

Remember, angular momentum is a vector quantity, so make sure to include the correct direction in your answer. In this case, the direction of the angular momentum would be perpendicular to both the velocity and the radius of the orbit.

I hope this helps! Good luck with your calculations.