Physics ANGULAR DISPLACEMENT AND ANGULAR VELOCITY

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ANGULAR DISPLACEMENT AND ANGULAR VELOCITY

Angular Displacement

`text(Angular Position :)`
The angle made by the position vector of a particle undergoing circular motion with a given line (reference line) is called angular position.

Suppose a particle P is moving in a circle of radius r and centre O.

The position of the particle P at a given instant may be described by the angle `theta` between OP and OX. This angle `theta` is called the angular position of the particle.

`text(Angular Displacement :)`
Angle rotated by a position vector of the moving particle with some reference line is called angular displacement.

a. Infinitesimal angular displacement is a vector quantity but finite angular displacement is not.
b. Direction of infinitesimal angular displacement is decided by right hand thumb rule.

`text(Angular Position :)`
The angle made by the position vector of a particle undergoing circular motion with a given line (reference line) is called angular position.

Suppose a particle P is moving in a circle of radius r and centre O.

The position of the particle P at a given instant may be described by the angle `theta` between OP and OX. This angle `theta` is called the angular position of the particle.

`text(Angular Displacement :)`
Angle rotated by a position vector of the moving particle with some reference line is called angular displacement.

a. Infinitesimal angular displacement is a vector quantity but finite angular displacement is not.
b. Direction of infinitesimal angular displacement is decided by right hand thumb rule.

Angular Velocity

(i) `text(Average Angular Velocity :)`
If `theta_1` and `theta_2` are angular position of the particle at time `t_1` and `t_2`.

`omega_(avg)=text(Total angle of rotation)/text(Total time taken)`

`=>omega_(avg)=(theta_2-theta_1)/(t_2-t_1)=(Deltatheta)/(Deltat)`

(ii) `text(Instantaneous Angular Velocity :)`
The rate at which the position vector of a particle w.r.t. the centre rotates at a given instant, is called its instantaneous angular velocity.

`:.` instantaneous angular velocity `omega=lim_(Deltat->0)(Deltatheta)/(Deltat)=(d theta)/(dt)`

(i) `text(Average Angular Velocity :)`
If `theta_1` and `theta_2` are angular position of the particle at time `t_1` and `t_2`.

`omega_(avg)=text(Total angle of rotation)/text(Total time taken)`

`=>omega_(avg)=(theta_2-theta_1)/(t_2-t_1)=(Deltatheta)/(Deltat)`

(ii) `text(Instantaneous Angular Velocity :)`
The rate at which the position vector of a particle w.r.t. the centre rotates at a given instant, is called its instantaneous angular velocity.

`:.` instantaneous angular velocity `omega=lim_(Deltat->0)(Deltatheta)/(Deltat)=(d theta)/(dt)`

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