To understand the meaning of the variables that appear in the equations for rotational kinematics with constant angular accelera
tion. Rotational motion with a constant nonzero acceleration is not uncommon in the world around us. For instance, many machines have spinning parts. When the machine is turned on or off, the spinning parts tend to change the rate of their rotation with virtually constant angular acceleration. Many introductory problems in rotational kinematics involve motion of a particle with constant, nonzero angular acceleration. The kinematic equations for such motion can be written as
Rotational kinematics can be treated as equivalent to linear kinematics, for this change the displacement will change to the angular displacement, the velocity to the angular velocity and the acceleration to the angular relation, that is
x → θ
v → ω
a → α
with these changes the three linear kinematics relations change to
ω = ω₀ + α t
ω² = ω₀² + 2 α θ
θ = θ₀ + ω₀ t + ½ α t²
where it should be clarified that to use these equations the angles must be measured in radians
