# Express the angular momentum of a marble

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Definition 1: The linear momentum, vector p, of an object is its mass, m, times its velocity, vector v.

Definition 2: The angular momentum, vector L, of an object about an axis, is defined as the cross product of the position, vector R, relative to the axis, and its linear momentum, vector p.

Definition 3: The magnitude of the cross product is the product of the magnitudes of the vectors times the sine of the angle between their positive directions.

The cross product is a vector perpendicular to both vectors.

Problem:

A marble of mass m moves with velocity v in the x,y plane at angle B relative to position vector R from origin to the mass.

SEE ATTACHMENT #1 PART a for a diagram of the parameters named above.

PART a. From definitions 1 and 2 above, write expressions for the linear momentum and for the angular momentum of the marble about the z axis.

PART b. Write a non-vector equation expressing the magnitude of the marble in terms of its mass, speed, position, and the angle B, then use values as follows to calculate its magnitude: m= .012 kg, R= 1.5 m, v= 48 m/sec, and B= 37 degrees.

PART c. Now the same marble is moving in a circle of radius R about the z axis with the same speed along the circumference. SEE ATTACHMENT #1 PART c. Find the angular momentum about the z axis at the center of the circle.

PART d. Write in terms of the angular velocity, the angular momentum of a mass m moving in a circle of radius R.

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