The angular acceleration α of a rotating body is its rate of change of angular velocity ω. If a small angular velocity change δω change occurs in a small time interval δ t, the angular acceleration α is given by:
α = limδ t ->0(δωδ t) = d ω dt
and is measured in rad s-2. The equations for uniform linear acceleration have rotational analogue which are:
where < v > is the average velocity, ω0 is the initial angular velocity and ω is the finial velocity (both in rad s-1 after the body has rotated through angular displacement θ (rad) with constant angular acceleration α (rad s-2 in a time interval t(s).
Power
Power is defined as the rate at which work is done.
If we replace the eqn for work, W= F.δs in (1) the power, the power is then P=F.(δs/δt), we recognise that δs/δt is the average velocity, v therefore, work is also, P= F.v.
The unit of power is the Joule per second, [J.s-1] which is more commonly called a Watt [W]. Another unit commonly used to measure power, especially in everyday situations, is the horsepower, which is equivalent to about 746 Watts. The rate at which our automobiles do work is measured in horsepower.
