The rigid body is an idealization of a solid body where the deformations occurring on the body are neglected. In other words, the distance between any two given points of a rigid body remains a constant regardless of the external force acting upon it. The two types of motion a rigid body can undergo are;
- Translational Motion
- Rotational Motion
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Moment of Inertia
Moment of Inertia is defined as the capacity of the system to oppose the change produced in the rotational motion of the body.
For a single particle moment of inertia I=mr2
Here m is the mass of the particle and r is the perpendicular distance from the axis about which moment of inertia is to be calculated.
For many particles, I = miri2
Moment of Inertia of different objects
Radius of Gyration
K = √I/M
Here
M is the mass of the rotating object
I is the moment of inertia
Relation Between Torque and Moment of Inertia
Ï„ is the torque (twisting effect of force)
I is the moment of inertia
α is the angular acceleration ( the rate of change of angular velocity)
Angular momentum
Point object: For an object accelerating around a fixed point. For example, Earth revolving around the sun. Here the angular momentum is given by:
L is the angular velocity
r is the radius
p is the linear momentum
Extended object:Â The object, which is rotating about a fixed point. For example, Earth rotating about its axis. Here the angular momentum is given by
ω is the angular velocity
L = angular momentum of the object
IÂ = Moment of inertia
Relation between angular momentum and Torque
Torque is the change in angular momentum
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