# Mechanics problem

If a rigid homogeneous rectangular crate of mass m and height h slides on its base of w, while traveling a velocity v, it stikes a low, immovable curb. What is the angular velocity of the crate immediately after the impact, in terms of m,w,h,v; and under what condition (in m,w,h,v) will the crate fall over on its side?

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...NTUM:

<br>the easiest thing is to calculate the angular momentum with respect to an axis passing through the ball, horizontal and perpendicular to the velocity of the crate (see picture 2).

<br>just as a remind, the angular momentum is the linear momentum multiplied by the distance to the center (the ball in this case).

<br>initial angular momentum = mvh/2 = Iy = final angular momentum

<br>where y is the angular speed (normally called omega), and I is the moment of inertia of the crate respect to the axis passing throught the ball.

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<br>I, respect to the ball (at the corner of the crate), is equal to I respect to the center of mass + m times the distance from the center of mass to the corner squared ...