For a more slowly rotating wheel, moving only a small fraction of a revolution in a second, it might be more convenient to measure the rotational speed in degrees per second, with 360 degrees being a complete revolution. Evidently, any formula of this kind relating speed of the mass to angular speed contains a 2 p on top and a number on the bottom stating how many of the angle units fit around one circle. The way to get the simplest possible formula is to choose a unit of angle such that 2 p of them fit around a circle, so the 360 in the formula above will be replaced by a 2 p , which will then cancel the 2 p on top. This unit of angle is called the radian , and is about 57 degrees. From now on, we shall measure angles in radians unless explicitly stated otherwise, and we shall use the standard symbol for angular velocity, w radians per second.
Radians are also a natural unit of angle for trigonometry.
As we have discussed above, if a body at rest is free to rotate about an axis, but the total torque of the forces acting on the body is zero, the body will be in rotational equilibrium and will remain at rest. It is also found experimentally that a body rotating at an angular velocity w will continue to rotate at that rate if the net torque is zero. These findings are the angular equivalents of Newton's First Law. Let us assume the mass is initially at rest, then the force F is applied. As soon as it reaches a significant speed, the disk will begin to exert a force towards the center, to keep it on its circular path, but let's just concentrate on the first few moments before that effect becomes important.