Conceptualize the linear momentum of the particle is changing in direction (but

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Conceptualize the linear momentum of the particle is changing in direction (but not in magnitude). You might therefore be tempted to conclude that the angular momentum of the particle is always changing. in this situation, however, that is not the case. Let's see why. Categorize We use the definition of the angular momentum of a particle discussed in this section, so we categorize this example as a substitution problem. A particle moving in a circle of radius r has an angular momentum about an axis through O that has magnitude mvr. The vector L = r times P points out of the page. Use the equation, L = mvr sin Phi, to L = mvr sin 90 degree = mvr evaluate the magnitude of L: This value of L is constant because all three factors on the right are constant. the direction of L also is constant, even though the direction of P = mv keeps changing. To verify this statement, apply the right- hand rule to find the direction of L = r times P = m (r times v) in the figure. Your thumb points upward and away from the page, so that is the direction of L. Hence, we can write the vector expression L = (mvr)k. If the particle were to move clockwise, L would point downward and into the page and L = - (mvr)k. A particle in uniform circular motion has a constant angular momentum about an axis through the center of its Rewrite the equation L in terms of the angular velocity omega rather than the linear speed nu. (Use m for the mass of the particle, for the radius, and omega for the angular velocity. L =

Explanation / Answer

L = r x P

L = m*v*r k

using the relation ,

speed v = rw

L = m*r*w*r k

L = m*r2*w K

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