Uniform circular motion

If a material point covers arcs of equal length in any equal time intervals along a circle, its motion is called uniform circular motion; here “uniform” refers to the magnitude of the velocity, while its direction keeps changing. The quantity numerically equal to the path a point covers along the arc per unit time is the linear speed: υ = s/t, where s is the arc length. As the point moves, the radius drawn to it from the centre turns through an angle φ — the angle of rotation, measured in degrees or radians. A central angle whose arc is equal in length to the radius is 1 radian (1 rad ≈ 57°); so φ = s/R, half a circle is π ≈ 3.14 rad and a full circle is 2π rad. How fast the radius turns is shown by the angular velocity: divide the angle of rotation by the time it took, ω = φ/t; the unit is rad/s. All points of a rotating rigid body have the same angular velocity, but points farther from the centre cover longer arcs in the same time, i.e. their linear speed is greater.