System of Particles and Rotational Motion: Comparison of Translational and Rotational Quantities (For CBSE, ICSE, IAS, NET, NRA 2022)

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  • A rigid body is a body with a perfectly definite and unchanging shape.
  • The combination of rotational motion and the translational motion of a rigid body is known as rolling motion.
  • The distances between all pairs of particles of such a body do not change.
  • According to the law of conservation of angular momentum, if there is no external couple acting, the total angular momentum of a rigid body or a system of particles is conserved

What is Translational Motion?

Translational Motion
  • Translational motion is the motion by which a body shifts from one point in space to another.
  • Let՚s imagine a rectangular block placed on the slanting edge of a right-angled triangle.
  • If the block is assumed to slide down this edge without any side movement, every point in the rectangular block experiences the same displacement and more importantly, the distance between the points is also maintained
  • Translational motion is motion that involves the sliding of an object in one or more of the three dimensions: x, y or z
  • In a pure translational motion, every point in the body experiences the same velocity be it at any instant of time.
  • Both the points, P1 and P2 undergo the exact same motions.
  • A car moving in a straight line, the path of a bullet out of a gun etc are examples of translational motion.

What is Rotational Motion?

Rotational Motion
  • Imagine a circular block going down the edge of the right-angled triangle.
  • Examining the location and orientation of different points on the cylindrical block will tell us something new.
  • A rigid body performs a real rotational motion if each particle of the body moves in a circle, and the center of all circles lies on the straight line (axis of rotation) .
  • The points on the cylindrical body experience something much different than the rectangular block.
  • As shown by the arrows in the diagram representing the velocity, each point experiences a different magnitude of velocity in a different direction. Here the points are arranged with respect to an axis of rotation.
  • Rotation is what you achieve when you constrain a body and fix it along with a straight line.
  • This means that the body can only turn around the line, which is defined as rotational motion.
  • Examples:
    • Rotation of ceiling fan.
    • Rotation of blades of a windmill.
    • Rotation of wheels of a car.

Comparison of Translational and Rotational Quantities

Translational and Rotational Quantities