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Explain with defination of angular position, angular displacement and angular speed for the motion of rigid body. |
Answer» Solution :In the figure a rigid body is rotating about a fixed axis Oz, normal to the plane of the figure.  All the particles of a rigid body move along CIRCULAR path and the centres of all these CIRCLES fall on a axis of rotation. Circular path is perpendicular to the axis. Suppose P is any particle of rigid body. This moves with radius (perpendicular distance from axis) r and about centre C of a circle. The linear velocity of particle at point P is `vecv` and is in the direction of tangent at point P. Suppose at `t=0` time particle is at P and at time `t+Deltat` it is on P. `therefore` ANGULAR displacement in `Deltat` time `=anglePCP` =`Deltatheta` In this time interval average angular velocity of particle `ltomegagt =(Deltatheta)/(Deltat)` As `Deltat` is small and when `Deltat` is near to zero then `(Deltatheta)/(Deltat)` is CALLED instateneous angular velocity `therefore` Instanteneous angular velocity is known as angular velocity also `therefore` Angular velocity `omega=underset(Deltatrarr0)lim(Deltatheta)/(Deltat)` `therefore omega=(d theta)/(dt)` Defination of angular position : The angle made by the line joining a particle with the centre of its circular path at a given time, with a given fixed REFERENCE line is called the angular position of the particle at that time. It is denoted by `theta` and it is scalar. Angular displacement : The change in angular position of a particle of rigid body is called angular displacement. It is denoted by `Deltatheta`. It is a vector. Angular velocity : time rate of change of angular position of a rigid body is known as angular velocity or instanteneous angular velocity. It is denoted by `omega` and it is vector. |
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