# Mass and Angular Acceleration

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• Published : February 10, 2013

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A small cube (m=0.690 kg) is at a height of 297.0 cm up a frictionless track which has a loop of radius, R = 38.61 cm at the bottom. The cube starts from rest and slides freely down the ramp and around the loop. Find the velocity of the block when it is at the top of the loop.

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b) A uniform solid cylinder (m=0.690 kg, of small radius) is at the top of a similar ramp, which has friction. The cylinder starts from rest and rolls down the ramp without sliding and goes around the loop. Find the velocity of the cylinder at the top of the loop.

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Problem 3|

A beam is supported only at one point, called the pivot point, as shown in the diagram. A block with mass m1 sits at the left end of the beam, a distance L1 from the pivot point. A block with mass m2 sits at the right end of the beam, a distance L2 from the pivot point. L2 > L1. Calculate all torques about the pivot point, remembering that positive is anti-clockwise.  Select Yes, No, Less than, Equal to, or Cannot tell.

If m1 * L2 = m2 * L1, is there a negative torque?         Given particular values of L1, L2, and m1, is it always possible to choose m2 such that the masses have no angular acceleration?         For m1 = m2, does the angular acceleration depend only on L1 / L2 ? (If it depends on the actual values of L1 and L2, put 'no'.)         If m1 = m2, will the masses have an angular acceleration?

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If L1 = 0.490 m, L2 = 1.18m, m1 = 4.10 kg, and m2 = 3.40 kg, what is the angular acceleration of the beam?
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Problem 4|

A 1.42 kg particle moves in the xy plane with a velocity of v = (4.26i - 3.43j) m/s. Determine the particle's angular momentum when its position vector is r = (1.49i + 2.36j) m. Enter the k-component of the angular momentum with correct units.

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