Terms and Formulae
Terms
Torque
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The rotational analogue to force.
Moment of Inertia
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The property of an object that dictates its angular
acceleration.
Rolling Without Slipping
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The special case of combined rotational and translational motion in which the
part of the object in contact with the ground has zero velocity.
Formulae
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Definition of torque
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τ = Fr sinθ
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Vector definition of torque
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τ = r×F
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Relation between τ and α
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τ = mr2α
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Rotational Analogue to Newton's Second Law
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τ = Iα
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Definition of work in angular motion
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W = τφ
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Integral definition of work in angular motion
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W = τdφ
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Definition of kinetic energy in angular motion
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K = Iω2
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Definition of power in angular motion
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P = τω
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Relation between linear and angular
velocity when an object
is rolling
without slipping
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vcm = ωr
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Kinetic energy when an object rolls without slipping, in terms of v
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K = mv2 + I
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Kinetic energy when an object rolls without slipping, in terms of ω
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K = mω2r2 + Iω2
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Formula for the moment of inertia of a rigid body
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I = r2dm
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