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A mechanical arm moves in a circle, causing a thin mirror to roll along a floor. The mirror has a radius 2 m and mass 1 kg and is connected to an arm that is 1.4 m long. The fixed point at the base of the arm should be considered the origin O and the center of the mirror should be considered the center of gravity G, so that the vector OG = 1.4m. The mirror is rolling at the rate of 27 rads/s about G, which acts as an axle. Find the angular velocity of the mirror. w G The units on the angular velocity are Find the angular momentum about the mounting point O. H it The units on the angular momentum are
H. 2 + The units on the angular momentum are Find the kinetic energy. KE = (units go in the second box). Find the angular momentum about the center of gravity on the plate. HG i + with units Find the angular velocity relative to the frame of motion. Ω ġ with units The derivative of the angular momentum is the relative sum of moments. We can get that HG = k with units Now, we can get the normal force on the mirror, which is 6 3 (units). Our reactions on the mirror as a result of rolling are R Jit 3 with units