Systems of Particles and Rotational Motion – II

Knowledge of the system of particles and rotational motion in class 11 is important from an examination point of view. To do well on any test, it is critical to understand the topic of rotational motion in class 11. 

In this article, we’ll go over translational motion, the concept of rigid body and its motion, the centre of mass, and rotational motion. Here also discusses some common questions from systems of particles and rotational motion.

Translational motion

Let’s look at some instances to understand translational motion fully. Consider a rectangular block put on a right-angled triangle’s slanting edge. Every point in the rectangular block experiences the same displacement. More significantly, the distance between the points is retained if the block is supposed to glide along this edge without any side movement.

Every point in the body experiences the same velocity in a pure translational motion, regardless of time. Consider the points P1 and P2 on a body. Both will go through the same motions. Translational motion can be illustrated by the examples of a car travelling in a straight line, the path of a bullet fired from a gun, and so on.

Rigid body

A rigid body has a well-defined shape that cannot be changed. A rigid body’s distance between its different pairs cannot be altered. As a result, no physical body is fully rigid, as most of them deform due to the influence of forces. However, there are cases where deformations are minor. 

Wheels, beams, steel, planets, and molecules are examples of objects that can be called rigid even though they wrap, vibrate, or bend. Furthermore, we are studying the various types of motion that a rigid body can have; this subtopic is also covered in the rotational motion class 11.

The motion of a rigid body

A few examples can describe the motion of a system of particles and a rigid body.

Rectangular block

Consider a rectangular block sliding down an inclined surface without moving sideways. The block is a rigid body that moves down the plane in such a way that all of the body particles move in lockstep. This indicates that all particles have the same velocity at any one time. As a result, this rigid body moves in a pure translational motion. It may be concluded that in pure translational motion, all body particles have the same velocity at any given time.

Solid wooden or metallic cylinder

In this case, we are using the same inclined plane as before to represent the rolling motion of a solid wooden or metallic cylinder. Here, the cylinder is a rigid body that shifts from the top to the bottom of the inclined plane, displaying translational motion. However, at any given time, all of the particles in this body do not move at the same speed. As a result, the cylindrical body isn’t in a state of pure translation. In addition to the translation motion, there is something else.

You can understand this additional phenomenon by confining a rigid body to prevent it from moving in any direction. It can be fixed in place along a straight line (rotation axis), and the only motion it can exhibit is rotation. For example, in a potter’s wheel or a ceiling fan.

Rotational motion

Rotation occurs when a rigid body circles around a fixed axis. Each particle moves in a circular motion in a plane perpendicular to the axis with its centre on the axis. Let’s have a look at an example to understand this better. 

Consider a circular block that goes along the right-angled triangle’s edge. We can learn something new by looking at the location and orientation of various spots on the cylindrical block. The points on the cylindrical body are subjected to a set of circumstances, distinct from the rectangular block. Each point is subjected to a different magnitude and direction of velocity. The points are organised around a rotational axis.

You can observe rotation when you limit a body and fix it along a straight line. This means that the body can only rotate around the line (rotational motion). Rotational motion can be found in a ceiling fan, a vehicle’s wheel, or a potter’s wheel.

Centre of mass

Following a series of studies, it was determined that the centre of mass of a system of particles moves as if all of the system’s mass was concentrated at its centre and all external forces were applied there. It was also known that a system of particles’ total momentum is equal to the product of the entire mass of the body or system and the velocity of its centre of mass.

The dynamics of a rigid body

Angular Displacement 

The angular displacement of a rigid body rotating around a fixed axis is the angle displaced by a line passing through a point on the body and intersecting the axis of rotation perpendicularly. It can rotate in either a counterclockwise (positive) or a clockwise (negative) direction.It’s the same thing as a displacement vector component.

Radian is the SI unit for angular displacement.

Angular Velocity

Angular velocity refers to the average angular velocity, either positive or negative. It is a vector quantity with a perpendicular direction to the plane of rotation. A particle’s angular velocity changes at different places. All particles in a rigid body have the same angular velocity around a point.

It denotes the rate at which an object rotates or revolves concerning another point or the speed at which a body’s angular position or orientation varies over time.

Conclusion

The centre of mass for a system of particles is the  point where the entire mass of the system is imagined to be concentrated, for consideration of its translational motion. A rigid body has a perfectly definite and unchanging shape, with the distances between all pairs of particles in it remaining unchanged.