Angular Momentum of a Rotating Particle

u

0

v

0

θ

0.1

time

0.1

axis labels

vector labels

Applying a torque to a particle about a given axis imparts an angular momentum that is not necessarily along the same axis. This is illustrated in this Demonstration for a particle of unit mass. You can vary the initial particle position

r=(cosθ,0,sinθ)

and the angular velocity vector

ω=(sinucosv,sinusinv,cosu)

. The position vector

r

(indicated by the black sphere), the velocity

v=ω×r

, and the angular momentum

L=r×v

all rotate as a function of time about the axis

ω

.

Details

The rotation of the particle is performed using the Mathematica built-in function RotationMatrix.

For more information, see Chapter 10 in[1] and Chapter 11 in[2].

References

[1] J. R. Taylor, Classical Mechanics, Sausalito, CA: University Science Books, 2005.

[2] S. T. Thornton and J. B. Marion, Classical Dynamics of Particles and Systems, Belmont, CA: Brooks/Cole, 2004.

External Links

Angular Momentum of a Rotating Rigid Body

Permanent Citation

Frederick W. Strauch

"Angular Momentum of a Rotating Particle" from the Wolfram Demonstrations Project http://demonstrations.wolfram.com/AngularMomentumOfARotatingParticle/
Published: August 9, 2011