Kinematics

Kinematics is that branch of mechanics which deals with the study of motion of objects without taking into account the factors (i.e. nature of forces, nature of bodies etc.) which cause motion.

Rectilinear motion is that motion in which a particle or point mass body is moving along a straight line.

Translatory motion is that motion in which a body, which is not a point mass body is moving such that all its constituent particles move simultaneously along parallel straight lines and shit through equal distance in a given interval of time e.g. A body slipping along the inclined plane has translatory motion.

Rectilinear or translatory motion can be uniform or non-uniform.

A circular motion is that motion in which a particle or a point mass body is moving on a circle.

A rotatory motion is that motion in which a body, which is not a point mass body is moving such that all its constituent particles move simultaneously along concentric circles, whose centers lie on a line, called axis of rotation and shift through equal angle in a given time.

If the circular or rotatory motion is uniform, it is periodic also.

If in the oscillatory motion, the amplitude is very small i.e. microscopic, the motion of body is said to be a vibratory motion.

Points

  1. The velocity in uniform motion does not depend upon the time interval. the velocity in uniform motion is independent of choice of origin.
  2. No force is required for an object to be in uniform motion.
  3. The average and instantaneous velocities have same value in uniform motion.
  4. The speed of the body can never be negative. The slope of velocity-time graph of uniform motion is zero.
  5. If the two bodies are moving with unequal uniform velocities, then their position time graphs must intersect each other.
  6. The speedometer of an automobile measures the instantaneous speed of the automobile.
  7. In case of uniform circular motion of an object, an object can have constant speed but variable velocity.
  8. When the velocity of the object is negative, the position time graph can also be negative.
  9. A body cannot have constant velocity and variable speed.
  10. When a body move with a uniform velocity i.e. there is a uniform motion of the body in one dimension then the average velocity becomes equal to instantaneous velocity.
  11. In a non- uniform motion of an object, the velocity of the object is different at different instants. such a motion is said to be an accelerated motion.
  12. If an accelerated motion, if the change in velocity of an object in each unit of time is constant, the object is said to be moving with constant acceleration and such a motion is called Uniformly accelerated motion.
  13. A body can have zero velocity and finite acceleration when a body is thrown vertically upwards in space, then at the highest point, the body has zero velocity but acceleration equal to the acceleration due to gravity. It is also the reason behind the direction of velocity of a body change, when acceleration is constant.
  14. Acceleration of a car is greater when brakes pedal is pushed hard, because car suddenly comes to rest i.e. the rate of change of velocity of car is large.
  15.  It is possible to have a constant rate of change of velocity (acceleration) when velocity changes both in magnitude and direction in Projectile motion.
  16. If the acceleration of the particle is constant in magnitude but not in direction then it is a circular path.
  17. It is the velocity that decide the direction of motion of the body.
  18. It is not possible to round a curve with acceleration because for a motion around a curve, there is a change in the direction of motion at every point of motion, which is only possible by a force and hence by an acceleration.
  19. Tensor: a physical quantity is said to be tensor if it is neither a scalar not a vector as its direction is not properly specified, but has different values in different directions. example: stress; moment of inertia;
  20.  Projectile is the name given to a body thrown with some initial velocity with the horizontal direction and then allowed to move in two dimensions under the action of gravity alone, without being propelled by any engine or fuel.
  21. When the particle describes a uniform circular motion, its speed is constant but it has centripetal acceleration acting along the radius directed towards the center of the circular path.
  22. Flight of rocket is not an illustration of projectile because it does not move under the gravity alone.
  23. When initial velocity gets double the projectile horizontal range becomes 4 times.
  24. In projectile motion, horizontal component velocity and total mechanical energy of projection remain constant throughout the motion.

 

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