In this problem, you will consider several changes to the situation at right. Al

Question

In this problem, you will consider several changes to the situation at right. All Original changes will be made explicit (i.e., if any quantities are not explicitly mentioned situation they do not change). In the situation at right, a puck of mass m is moving to the right with velocity vo across a level, frictionless table. In this problem, take all angular momenta with respect to the point marked by the "X." a. If the speed of the puck were initially twice as large, would the magnitude of the angular momentum be greater than, less than, or equal to that in the original situation? Explain b. If instead the puck were initially closer to the disk, as shown at right, would the magnitude of the angular momentum be greater than, less than, or equal to that in the original situation? Explain. c. If instead the puck were initially closer to the top of the page as shown, would the magnitude of the angular momentum be greater than, less than, or equal to that in the original situation? Explain. d. If instead the puck were more massive, would the magnitude of the angular 2m momentum be greater than, less than, or equal to that in the original situation? Explain. e. Suppose that the puck were both closer to the top of the page as shown and 2m twice as massive. Would the magnitude of the angular momentum be greater than, less than, or equal to that in the original situation? Explain.

Explanation / Answer

a)

Angular momentum is given as

L = m v r     ,

m = mass

V = speed

r = distance from point of rotation

as we make the speed double , the magnitude of angular momentum also gets doubled.So angular momentum becomes greater than the angular momentum in original situation.

b)

The angular momentum will not change since the perpendicular distance from point 'x' is unchanged. so 'r' remains unchanged which keeps angular momentum unchanged.

So angular momentum becomes equal to the angular momentum in original situation.

c)

As the puck goes closer , the value of 'r' decreases. and as 'r' decreases , Angular momentum decreases according to the formula above. So the angular momentum becomes less than the angular momentum in original situation.

d)

A more massive puck means a larger value of "m" . According to the formula above , as "m" increases , the angular momentum increases in same proportion.

So angular momentum becomes greater than the angular momentum in original situation.

e)

m is made "2m"

r is made "r/2"

New angular momentum = 2m x V x (r/2) = m V r

So we see that angular momentum comes out to be the same as before.

So angular momentum becomes equal to the angular momentum in original situation.

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