Mechanics
Linear-Angular Velocity Relation
Relates linear and angular velocities.
Variables
vm/s
Linear velocity
Tangential speed
rm
Radius
Distance from axis
ωrad/s
Angular velocity
Rate of rotation
Derivation
Arc length s = rθ, differentiate: v = ds/dt = r(dθ/dt) = rω.
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Common questions
What is the Linear-Angular Velocity Relation formula?
Linear-Angular Velocity Relation is written v = rω. Relates linear and angular velocities. It belongs to Mechanics, under Rotational Motion.
What are the units in v = rω?
In SI units, v is linear velocity, measured in m/s; r is radius, measured in m; ω is angular velocity, measured in rad/s.
How is the Linear-Angular Velocity Relation formula derived?
Arc length s = rθ, differentiate: v = ds/dt = r(dθ/dt) = rω. The result is v = rω.