Rotational Kinematics
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The Rotational Variables: |
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The variables which need to be dealt in rotational motion are discussed below.
(i) angular position (θ) is given by,
where ‘s’ is the arc length and ‘r’
is the radius of the circular path.
(ii) angular displacement Δθ given by,
where θ1 and θ2 are the initial and final angles created at the centre of the circular path.
(iii) The angular velocity is used to describe how quickly an object is rotating. It is measured in
rad/s and is symbolized by the Greek letter omega (ω).
The angular velocity is now given by,
Thus, the angular velocity is the first derivative of the angular position, just as velocity is the first
derivative of position.
Since ,
Now we can write:
The linear velocity is given by the rate of change of displacement:
Thus, we finally obtain:
or 
(iv) Average angular acceleration is the change in angular velocity divided by the time in which it
occurs.
If we take the limit of this as Δt approaches 0,
this equation becomes:
Thus, the angular acceleration is the rate of change of angular velocity.
(v) The angular momentum L is a measure of the difficulty of bringing a rotating object to rest.
L = Iω
Where, I is the moment of inertia of the rotating object and
ω is its angular velocity. Angular
momentum is a conserved quantity. In an isolated system it remains the same.
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Newtonian Mechanics