Two uniform cylinders are made of the same material, have the same thickness, an
ID: 1450950 • Letter: T
Question
Two uniform cylinders are made of the same material, have the same thickness, and arc rotating about their axes of symmetry. Cylinder B has twice the radius of Cylinder A. Recall that the moment of inertia of a cylinder of mass M and radius R that is rotating about its axis of symmetry is If the two cylinders arc to have the same angular momentum, what must be the relation between their angular speeds w_a and w_b? If the two cylinders are to have the same rotational kinetic energy, what must be the relation between their angular speeds w_a and w_b?Explanation / Answer
a) Ia wa = Ib wb
(Mass = M = rho V = rho x pi x r^2 x h)
(Ma r / 2) wa = (mb 2r / 2) wb
(((rho x pi x r^2 x h) x r) / 2) wa = (((rho x pi x (2r)^2 x h) x 2r) / 2) wb
r^2 wa = 4r^2 wb
wa = 4 wb (Answer)
b) 1/2 Ia wa^2 = 1/2 Ib wb^2
Ia wa^2 = Ib wb^2
(((rho x pi x r^2 x h) x r) / 2) wa^2 = (((rho x pi x (2r)^2 x h) x 2r) / 2) wb^2
r^2 wa^2 = 4r^2 wb^2
wa^2 = 4 wb^2
Squaring both sides
wa = 2 wb
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