Exam 10: Rotation

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A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR2.A light string of length 2.5 R is attached to the surface and used to suspend the sphere from the ceiling.Its rotational inertia about the point of attachment at the ceiling is:

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A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s2.By the time it stops it will have turned through:

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If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:

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Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A.The ratio of the magnitude of the radial acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is:

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A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery.Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s2.The cord will unwind in:

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A 0.70-kg disk with a rotational inertia given by MR2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling.A string is wrapped around the disk and a 2.0-kg mass hangs from the free end.If the string does not slip then as the mass falls and the cylinder rotates the suspension holding the cylinder pulls up on the mass with a force of:

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The angular speed of the second hand of a watch is:

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A wheel initially has an angular velocity of 18 rad/s.It has a constant angular acceleration of 2.0 rad/s2 and is slowing at first.What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity?

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A force is applied to a billiard ball.In order to calculate the torque created by the force, you also need to know:

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The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s.The speed of the point P is: The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s.The speed of the point P is:

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One-dimensional linear position is measured along a line, from a point designated x = 0.One-dimensional angular position:

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The angular velocity of a rotating turntable is given in rad/s by ω(t)= 4.5 + 0.64t - 2.7t2.What is its average angular acceleration between t = 1.0 s and t = 3.0 s?

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To increase the rotational inertia of a solid disk about its axis without changing its mass:

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Instantaneous angular speed is:

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The torque exerted on an object can be written as The torque exerted on an object can be written as   .Here,   : .Here, The torque exerted on an object can be written as   .Here,   : :

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A force with a given magnitude is to be applied to a wheel.The torque can be maximized by:

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A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s4)t2. It stops in a time of:

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A wheel starts from rest and spins with a constant angular acceleration.As time goes on the acceleration vector for a point on the rim:

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The angular velocity of a rotating turntable is given in rad/s by ω(t)= 4.5 + 0.64t - 2.7t2.What is its angular acceleration at t = 2.0 s?

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