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Unformatted text preview: 5‘0 L 3770 m
Physics 21 Midterm # 2 Winter 2009 1. (30 points) A wheel consists of a circular rim of radius R and mass M,
together with 6 spokes, each of mass M12, as shown. This wheel is placed
on an incline of angle 6, upon which it rolls without slipping. With what
acceleration does it move down the incline? (Treat each pair of spokes as a
thin rod, and recall that the moment of inertia of a thin rod of mass M and length L about its center is ML2 /12.) 0‘1 4 7L Hui m Mme parcf m far, So we
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f’fﬂ‘f flfv/f, A?" a“ All“ Mara work. 2. A plank of length L width W and mass M, is lying at rest on a horizontal
frictionless surface, as shown. A second identical plank is sliding across the
surface moving in the xdirection with speed V0, as shown. Just as the moving plank passes the resting plank, their ends are fused together (crazy
glue?) to make one long plank. The moment of inertia of such a plank about its center ofmass is M(L2 +W2)/12.‘ (a. 10 points) With what velocity (magnitude and direction) does the center
of mass of the combined planks move?.. (b. 15 points) With what angular velocity (magnitude and direction) do the
combined planks rotate? (c. 15 points) What fraction of the initial kinetic energy is lost in this
collision? tws t—ws ~ L
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U: {[l' $331 3. A thin rod of length 2a has a non—uniform density, which is lower near
the center of the rod and increases toward the ends of the rod. The linear density ﬁx), is given by 20:): 20(x/a)2, where 10 is a constant with
dimensions of kg/m, and xis the distance from the center of the rod. (This means that the mass 5m , of a short piece of the rod of length 6x , located a
distance x from the center of the rod is given by 6m = l(x)5x .) (a. 15 points) Calculate the mass M, of the rod. (b. 15 points) Calculate the moment of inertia of the rod about an axis
passing through its center, and express your result in terms of M and a. ...
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 Spring '08
 Freedman

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