# Tangential Velocity Formula

The tangential velocity is the velocity measured at any point tangent to a turning wheel. Thus tangential velocity, v_{t} is related to the angular velocity of the wheel, ω, and the radius of the wheel, r.

*V _{t} = ω r *

*V _{t}* = tangential velocity

*ω* = angular velocity

*r* = radius of wheel

Tangential Velocity Formula Questions.

1) If the angular velocity of a turning bicycle wheel is 42 rad/s, and the wheel diameter is 68 cm, what is the tangential velocity?

Answer: The radius, r = 1/2 diameter of 68 cm = 34 cm = 0.34 m. The angular velocity, ω = 42 rad/s. Use the equation for tangential velocity.

*V _{t} = ω r *

*V _{t}* = (42 rad/sec) x 0.34 m

*V _{t}* = 14.28 m/s

2) If a wheel is turning at 12 m/sec, and its angular velocity is 6 radians/sec, what is the radius of the wheel?

Answer: The tangential velocity, V_{t} = 12 m/sec. The angular velocity, ω, is 6 radians/sec. Use the formula for tangential velocity to find the radius, r.

*V _{t} = ω r *

*V _{t} / ω = r*

(12 m/sec)/(6 radians/sec) = *r*

*r* = 2 m

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