week7-3

week7-3 - 1J-29 Overhanging Blocks How far out from the...

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2/25/2011 1J-29 Overhanging Blocks IN REALITY EACH BLOCK HAS TO BE MOVED SLIGHTLY BACK TO AVOID TIPPING, SO THE TOTAL EXTENSION WILL BE A LITTLE LESS. How do the blocks stay balanced when the top block extends beyond the bottom block ? Blocks can over hang but the Center of Gravity of a block must be inside the block below Length = L, CG = L/2 Length = 3L/2, CG = 3L/4 Length = 7L/4, CG = 25L/24 Δ x For 6 blocks max extension Δ x : Δx = L/2 + L/4 + L/6 + L/8 + L/10 + L/12 = 1.22(L) How far out from the table can a stack of bricks be balanced ?

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Rotational Inertia and Newton’s Second Law In linear motion, net force and mass determine the acceleration of an object. For rotational motion, torque determines the rotational acceleration . The rotational counterpart to mass is rotational inertia or moment of inertia . Just as mass represents the resistance to a change in linear motion, rotational inertia is the resistance of an object to change in its rotational motion. Rotational inertia is related to the mass of the object. It also depends on how the mass is distributed about the axis of rotation .
Simplest example: a mass at the end of a light rod A force is applied to the mass in a direction perpendicular to the rod. The rod and mass will begin to rotate about the fixed axis at the other end of the rod. The farther the mass is from the axis, the faster it moves for a given rotational velocity.

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Simplest example: a mass at the end of a light rod To produce the same rotational acceleration, a mass at the end of the rod must receive a larger linear acceleration than one nearer the axis. F = ma It is harder to get the system rotating when the mass is at the end of the rod than when it is nearer to the axis. I case the distance are equal, it’s harder to move a heavier mass.
Second Law Newton’s second law for linear motion: F net = m a Newton’s second law for rotational motion: ܨ ௡௘௧ R = m ∆௩ ∆௧ ∙ ܴ ݒ = ߱ ∙ ܴ ܨ ௡௘௧ R = m ∙ ܴ ௗఠ ௗ௧ net

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week7-3 - 1J-29 Overhanging Blocks How far out from the...

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