# Linear Speed Formula (Rotating Object)

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From: drtjgunn.com

Linear Speed Formula (Rotating Object)

The linear speed of a point on a rotating object depends on its distance from the center of rotation. The angular speed is the angle that an object moves through in a certain amount of time. The angular speed has units of radians per second (rad/s). There are 2π radians in a full circle. At a distance r from the center of the rotation, a point on the object has a linear speed equal to the angular speed multiplied by the distance r. The units of linear speed are meters per second, m/s.

linear speed = angular speed x radius of the rotation

v = ωr

v = linear speed (m/s)

ω = angular speed (radians/s)

r = radius of the rotation (m)

Linear Speed Formula (Rotating Object) Questions:

1) A power drill is on, and spinning at 10.0 revolutions per second (rev/s). The diameter of the drill bit is 4.00 mm. What is the linear speed of a point on the surface of the drill bit, in meters per second?

a. V = ?.??? m/s

2)) A sensor is connected inside a car wheel, which measures the linear speed. The sensor is 0.080 m from the center of rotation. At that position, the sensor reads that the linear speed of the wheel is 8.00 m/s. If the radius of the wheel is 0.220 m, what is the linear speed on the outer edge of the wheel?

a. V = ??.? m/

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