A rigid body is defined as a solid body in which the molecules are compactly arranged so that the intermolecular distance is small and fixed such that their positions are not altered by any external forces acting on it and the shape of the body is always unaltered. A rigid body can go both translational and rotational motion.
In translational motion, the body displaces from one point to another such that every particle in it experiences same displacement and same linear velocity. For example; sliding of a wooden block.
In rotational motion, the body rotates from one point to another making concentric circles such that all the particles have the same angular velocity but different linear velocities. For example; the movement of wheels in automobiles.
S = r. θ
If the angular displacement is dθ in time interval dt, then angular velocity ω is defined as,
ω = dθ/ dt
if the angular velocity is not constant, the angular acceleration α is defined as,
α = dω/ dt
Along with angular velocity, the particles also have linear velocities. For the relation between the velocities,
v = ds/ dt
v = d r. θ/ dt
v = r dθ/dt
v = r. ω
The angular acceleration and linear acceleration are related as
a = dv/ dt = r dω/ dt = r. α
Therefore, we can conclude that angular quantities and linear quantities are related with each other.
Relation of equations of motion of rotational motion and linear motion
|
S. No. |
Equation of Rotational motion |
Equation of Linear motion |
|
1. |
ω = ω0 + α. t |
v = u + a. t |
|
2. |
θ = ω. T + ½ αt2 |
S = u. t + ½ at2 |
|
3. |
ω2 = ω02 + 2αθ |
v2 = u2 + 2as |
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