Motion

A disturbance that travels through the space or medium transferring energy without the net movement of particles is called a wave. Rather than moving along with the wave, the particles of the medium only oscillate about their mean position in a wave motion. The wave is fundamentally different as compared to the particle motion where the particles travel from one place to another. In a sound wave, the air molecules do not travel to the sound, they vibrate back and forth. The concept of wave motion is one of the most important concepts in knowing how energy is transmitted in various forms including light, sound and water waves.

Rolling motion is a combination of rotational and translation motion where an object moves forward while spinning around an axis. An example is a rolling wheel. The equation for rolling motion without slipping is:

v represents the linear velocity, r is the radius and w stands for the angular velocity. Rolling motion is more complex than pure rotation as in this case every point on the object follows a curved trajectory whereas in pure rotation, the object only spins around a fixed axis without any change in its position.

Torque (? ) is used to measure the force that causes rotational motion. It is similar to how force causes linear motion. Newton's second law for rotational motion shows the relation between torque and angular acceleration.

I stand for the moment of inertia and a is the angular acceleration. According to this equation, the greater the torque applied to an object, the higher its angular acceleration. Moreover, the object with a larger I will require more torque to achieve the same angular acceleration.

Moment of Inertia (I) is the rotational equivalent of mass and it is used to measure an object's resistance to changes in its rotational motion. I is based on the mass of the object and how it is distributed relative to the axis of rotation. The formula to measure the moment of inertia is - 

m stands for mass and r for the perpendicular distance from the axis. Similar to how mass plays a crucial role in linear motion, moment of inertia plays a significant role in rotational motion. The objects with higher I require more torque to achieve the same angular acceleration.

Translational motion is when every part of an object moves at the same speed and uniformly in the same direction, like a car moving along a straight road. Rotational motion refers to an object rotating around a fixed axis, eg- a spinning wheel. One of the main difference is that in translation motion, all points on the object have the same velocity and in rotational motion, velocity changes based on the distance from the axis of rotation. Various real-life motions combine both rotational and translation motion.

The centre of mass (COM) of a system refers to the point that represents the average position where the entire mass of the system is considered to be concentrated. The concept helps in analyzing the motion of a system of particles. Following is the formula to determine the COM of two or more particles:

In this formula,  m1, and m2 stand for masses and r1, r2 are their respective positions. COM motion follows Newton's law which says that if no external force acts on a system, COM moves with uniform velocity.