Rigid body is defined as a system of particles in which distance between each pair of particles remains
constant (with respect to time).
A body is said to be in pure translational motion, if the displacement of each particle of the system is same
during any time interval.
Pure Rotational Motion
Combined Translational and Rotational Motion
MOMENT OF INERTIA (I) ABOUT AN AXIS
TWO IMPORTANT THEOREMS ON MOMENT OF INERTIA
(Applicable to planer as well as 3 dimensional objects):
List of some useful formule
Thin rod
As a measure of the way in which the mass of rigid body is distributed with
respect to the axis of rotation, we define a new parameter, the radius of gyration
(K). It is related to the moment of inertia and total mass of the body.
A uniform disc of radius R has a round disc of radius R/3 cut as shown in Fig.
.The mass of the remaining (shaded) portion of the disc equals M. Find the
moment of inertia of such a disc relative to the axis passing through geometrical
centre of original disc and perpendicular to the plane
of the disc.
Torque represents the capability of a force to produce change
in the rotational motion of the body
The torque of a force ?
F about an axis AB is defined as the component of torque of ?
F about any
point O on the axis AB, along the axis AB.
A couple does not exert a net force on an object even though it exerts a torque
Point of Application of force is the point at which, if net force is assumed to be acting,
then it will produce same translational as well as rotational effect, as was produced
earlier.
Rotation about a fixed axis
A system is in mechanical equilibrium if it is in translational as well as rotational
equilibrium
Angular momentum of a particle about a point
Angular momentum of a rigid body rotating about fixed axis
Conservation of Angular Momentum
COMBINED TRANSLATIONAL AND ROTATIONAL
MOTION OF A RIGID BODY
For a rigid body as earlier stated value of angular displacement (?) , angular velocity (? ),
angular acceleration (?) is same for all points on the rigid body about any other point on the
rigid body
Pure Rolling (or rolling without sliding)
This motion can be viewed as translation of centre of mass and rotation about an axis
passing through centre of mass
It is the axis about which the combined translational and rotational motion appears as
pure rotational motion
Rolling on moving surface
In many situations an external force is applied to a body to cause it to slide along a
surface. In certain cases, the body may tip over before sliding ensues. This is known
as topping.
