A collision between two particles is defined as the mutual interaction between particles for a short interval of time as a result of which energy and momentum of the particle change. In the collision of two particles, the law of conservation of momentum always holds true but in some collisions, kinetic energy is not always … Read more
The center of mass for many particle system is given by, Differentiating the above equation, we get, But, $d(R_{CM})/dt=V_{CM}$= velocity of center of mass and $d(r_{i})/dt=v_{i}$= velocity of i’th particle of the system Therefore, ……………….. (1) Also, $m_{i}v_{i}$= momentum of i’th particle of the system. Then, $p$ is the vector sum of linear momentum … Read more
Center of mass is the point where the whole mass of the system can be supposed to be concentrated and the motion of the system can be defined in terms of the center of mass. Position of center of mass for the two-particle system: Consider a system of two point masses $m_{1}$and $m_{2}$,whose position vectors … Read more
Work is done when an object moves a distance by the application of a force. Consider a block placed on a frictionless horizontal floor. This block is acted upon by a constant force $F$ to move through a distance $d$ in a straight line in the direction of force. Work done is equal to the … Read more
1. A force is applied horizontally on a uniform rod of length L kept on a surface. Calculate the tension in the rod at a distance r from the end where the force is applied. Let the mass of rod be M, and applied force is F. Acceleration produced in the rod $a=F/M$ The free … Read more
Banking of Roads: When a car moves along a curved road, it requires some centripetal force. During the turn, the wheels of the car have a tendency to leave the curved path and regain the straight line path. The frictional force between the wheels and the road opposes this tendency of the wheels. Therefore, the … Read more
Concept of force: A force is a push or pull which changes or tends to change the state of rest or of uniform motion or direction of motion of any object. The SI unit of force is Newton (N). The force with which the earth attracts a 1 kg body towards its centre is called … Read more
1. The displacement of an object is given by the following equation. $x=2t+t^{2}_{}-3t^{3}$ Calculate the velocity of the object when its acceleration is zero. We have, $x=2t+t^{2}_{}-3t^{3}$ Or, velocity $v=\frac{dx}{dt}=\frac{d}{dt}(2t+t^{2}_{}-3t^{3})$ Or, $v=2+2t-9t^{2}$\ldots \ldots \ldots \ldots \ldots (1) Acceleration, $a=$$\frac{dv}{dt}=\frac{d}{dt}(2+2t-9t^{2})$ Or, $a=2-18t$ Or, $2-18t=0$, as acceleration is zero Or, $t=2/18=1/9$ Putting this value in equation (1), … Read more
When an object moves in a circular path at a constant speed, then the motion of the object is called uniform circular motion. In a uniform circular motion, the object accelerates because of the constantly changing the direction of the velocity. Centripetal acceleration: Let us consider an object moving in a circular path of radius … Read more
Projectile motion is a type of motion in which an object called a projectile is thrown or projected. It is an example of a two-dimensional motion with constant acceleration. The projectile is thrown with some initial velocity near the earth’s surface, and it moves along a curved path under the influence of gravity. There are … Read more