-When a rigid body rotates about a fixed axis, the angular displacement is the angle Δθ swept out by a line passing through any point on the body and intersecting the axis of rotation perpendicularly
-Can be positive (counterclockwise) or negative (clockwise).
-Analogous to a component of the displacement vector.
-SI unit: radian (rad). Other
units: degree, revolution.
Average angular velocity, is defined by
$ = (angular displacement)/(elapsed time) = Δθ/Δt .
Instantanous Angular Velocity ω=dθ/dt
-Angular velocity can be positive or negative.
-It is a vector quantity and direction is perpendicular to the plane of rotation
-Angular velcity of a particle is diffrent about diffrent points
-Angular velocity of all the particles of a rigid body is same about a point
Average angular acceleration, is defined by
= (change in angular velocity)/(elapsed time) = Δω/Δt
Instantanous Angular Acceleration
Kinematics of rotational Motion
ω=ω0 + αt
ω.ω=ω0.ω0 + 2 α.θ;
Vector Nature of Angular Variables
-The direction of an angular variable vector is along the axis.
- positive direction defined by the right hand rule.
- Usually we will stay with a fixed axis and thus can work in the scalar form.
-angular displacement cannot be added like vectors
-angular velocity and acceleration are vectors
Relation Between Linear and angular variables
Where r is vector joining the location of the particle and point about which angular velocity is being computed
Moment of Inertia
Rotational Inertia (Moment of Inertia) about a Fixed Axis
For a group of particles,
I = ∑mr2
For a continuous body,
I = ∫r2dm
For a body of uniform density
I = ρ∫r2dV
Parallel Axis Therom
Where Icc is the moment of inertia about the center of mass
Perpendicular Axis Therom
It is valid for plane laminas only
Class 9 physics notes on chapter motion is now available at the following link CLASS 9 MOTION NOTES (FULL LENGTH)
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