Formulas & tables/Physics/Kinematics/Linear velocity in circular motion

Linear velocity in circular motion

v=\omega r

Result unit: m/s

What it describes

The linear velocity of a point on a circle equals the angular velocity multiplied by the radius.

v

linear velocity

[m/s]

\omega

angular velocity

[rad/s]

r

radius

[m]

A point farther from the axis (larger

r

) covers a longer path in the same time, so it has a greater linear velocity for the same angular velocity.

Circular motion — converting angular velocity to linear velocity.

A point at

r=0.5

m rotates at

\omega=4

rad/s. Find its linear velocity.

Substitution

\omega=4

rad/s,

r=0.5

Result

v=4\cdot0.5=2

m/s.

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