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Just imagine the seat of the car having a faster velocity than the remaining parts of the car. Sounds funny, right? In translation, all the particles of the rigid body move along parallel paths, and if these parallel paths are straight lines, the motion is said to be a rectilinear translation.
If you notice, during the course of one full rotation, the part of the rod at point O remains fixed. Hence, as you can see, the different points of the rod have a different velocity.
One very important point to notice here is that all the points on the rod move in concentric circular paths only. A rigid body is considered to be in pure rotation only if each and every particle of the body moves in a circle, and the centers of all the circles lie on a straight line. This line is known as the axis of rotation A. In pure rotation, all points in the rigid body that are perpendicular to the A.
In the figure above, the A. General rigid body motion is a combination of pure translation and pure rotation. So, while solving a rotational mechanics question, try to break the motion of the body into translation and rotation, then solve for each of them.
Angular Velocity Have you ever rotated a ball tied to a thread? Think of swinging it in a circular motion above your head.
As we spin this ball around, we can observe the fundamentals of angular velocity! While rotating the ball, if the string is suddenly cut, in which direction will the ball go?
Will it still try to complete the circle or will it go tangentially? With what velocity will it go?
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Horizontal and Vertical Planes Consider the figure below. Notice how the circular motion in the picture is happening in a horizontal plane. A circular motion happening in a vertical plane is an altogether different ball game!
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It is basically the angle covered with respect to a baseline when an object rotates on an axis. The angular displacement happens on the same plane as that of the rotation of the object.
Depending on the time frame chosen to calculate the rate of change of angular displacement, angular velocity can be of one of the following two types. Average angular velocity: This is simply the rate of change of angular displacement with reference to the time measured over a time interval. Instantaneous angular velocity: It is defined as the rate of change of angular position with reference to the time at any instant of time.
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Definite Integration. After viewing the Study Material and along with all subjects PDF details regarding their exam syllabus, the candidates will be trying to find it from here soon. The faster particles would move farther and the car would be dismantled.
JEE Main online , , , and Question Papers with answer key and solutions are available to download for the students.