Will rate ,What should l à steady the angular acceleration of the axle be? lle a

Question

Will rate ,What should l à steady the angular acceleration of the axle be? lle akle must 2.25 cm/s when it is give the buckets an upward acceleration of 0.345 3) A centrifuge in a medical laboratory rotates at an angular speed of 2800 rpm (revolutions per minute). When switched off, it rotates 47.5 times before coming to rest. Find the constant angular acceleration of the centrifuge. (Assume the initial direction of rotation is the positive direction. Indicate the direction with the sign of your answer.) 4) A thin uniform rod (length 1.3 m, mass 4.1 kg) is pivoted about a horizontal frictionless pin through one of its ends. The moment of inertia of the rod through this axis is (1/3)ml2 The rod is released when it is 30° below the horizontal. What is the angular acceleration of the rod at the instant it is released? 5) Determine the moment of inertia for three children weighing 59.0 lb, 46.0 Ib and 84 lb sitting at t points on the edge of a rotating merry-go-round, which has a radius of 12 ft. 6) A 22-kg boy stands 5 m from the center of a frictionless playground mery-go-round, which has a moment of inertia of 238 kg m2. The boy begins to run in a circular path with a speed of 0.6 m/'s relative to the ground. (a) Calculate the angular velocity of the merry-go-round. (b) Calculate the speed of the boy relative to the surface of the merry-go-round. A circular saw blade 0.200 m in diameter starts from rest. In 4.00 s it accelerates with constant angular acceleration to an angular velocity of 150 rad/s. Find the angular acceleration and the angle through which the blade has turned. 7) an axis through its center. The disk has mass 150 kg and a radius of 3.0 m. Calculate the magnitude of the total angular momentum of the woman-plus-disk system. (Assume that you can treat the woman as a point.) A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of 19.0 kg m2. She then tucks into a small ball, decreasing this moment of inertia to 3.40 kg·m2. While tucked, she makes two complete revolutions in 1.0 s. If she hadn't tucked at all, how many revolutions would she have made in the 1.95 s from board to water? 8) A woman with mass 72 kg is standing on the rim of a large disk that is rotating at 0.40 revs about 9)

Explanation / Answer

Initial moment of inertia —> I = 19 kg • m ² …

Final moment of inertia —> I = 3.4 kg • m ² …

By conservation of angular momentum … I = I …

… where … = / t = 2 ( 2 rad ) / ( 1 s ) = 12.5664 rad / s …

so that … = I / I = ( I / I )

…….….…….….…….….… = ( 3.4 / 19 ) (12.5664 rad / s )

…….….…….….…….….… = 2.249 rad / s …

Similarly … = / t —> = t … that is …

… = ( 2.249 rad / s ) ( 1.95 s )

…….…. = 4.385 rad = ( 3.351032 rad ) / ( 2 rad / rev )

…….…. = 0.698 rev …

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