A Rigid Body

Classical Mechanics Level 1

Different particles on a rigid body have different linear speeds and tangential accelerations while their angular velocities and angular accelerations are the same.

True False

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1 solution

Matthew Murray
Jan 19, 2018

Linear speeds and tangential accelerations depend on where the body is relative to the axis of rotation while angular velocities and angular accelerations do not. This can be quickly seen by looking at their formulas.

Angular velocity: ω = d ϑ d t \frac{dϑ}{dt} Angular acceleration: α = d ω d t \frac{dω}{dt}

Linear speed: v = ω x R Tangential Acceleration: a = d v d t \frac{dv}{dt} = α x R

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