Reference Book is LINEAR MOMENTUM AND ITS CONSERVATION

Reference Book is

LINEAR MOMENTUM AND ITS CONSERVATION The linear momentum P of a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity: Linear momentum is a vector quantity because it equals the product of a scalar quantity m and a vector quantity v. Its direction is along v, it has dimensions ML/T, and its SI unit is kg m/s.

* Using Newton’s second law of motion, we can conclude that “ The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle”

Conservation of Momentum for a Two-Particle System Applying Newton’s second law to each particle, we can write Newton’s third law tells us that F 12 and F 21 are equal in magnitude and opposite in direction. That is, they form an action–reaction pair F 12 , F 21. We can express this condition as

Because the time derivative of the total momentum ptot p 1 p 2 is zero, we conclude that the total momentum of the system must remain constant: where pli and p 2 i are the initial values and p 1 f and p 2 f the final values of the momentum during the time interval dt over which the reaction pair interacts. Conservation of momentum Whenever two or more particles in an isolated system interact, the total momentum of the system remains constant.

SIMPLE HARMONIC MOTION An object moves with simple harmonic motion whenever its acceleration is proportional to its displacement from some equilibrium position and is oppositely directed. Applying Newton’s second law to the motion of the block, together with equation relates a force that is proportional to the displacement which is given by Hooke’s law , so :

In general, a particle moving along the x axis exhibits simple harmonic motion when x, the particle’s displacement from equilibrium, varies in time according to the relationship The period T of the motion : is the time it takes for the particle to go through one full cycle. The frequency: represents the number of oscillations that the particle makes per unit time The units of f are cycles per second s-1, or hertz (Hz).

THE PENDULUM When is small, a simple pendulum oscillates in simple harmonic motion about the equilibrium position θ. The restoring force is mg sin θ , the component of the gravitational force tangent to the arc.

if we assume that θ is small, we can use the approximation sin θ = θ ; thus the equation of motion for the simple pendulum becomes Therefore, can be written as Where θ max is the maximum angular displacement and the angular frequency is

The period of the motion is The period and frequency of a simple pendulum depend only on the length of the string and the acceleration due to gravity. The simple pendulum can be used as a timekeeper because its period depends only on its length and the local value of g. It is also a convenient device for making precise measurements of the free-fall acceleration.

The Foucault pendulum at the Franklin Institute in Philadelphia. This type of pendulum was first used by the French physicist Jean Foucault to verify the Earth’s rotation experimentally. As the pendulum swings, the vertical plane in which it oscillates appears to rotate as the bob successively knocks over the indicators arranged in a circle on the floor. In reality, the plane of oscillation is fixed in space, and the Earth rotating beneath the swinging pendulum moves the indicators into position to be knocked down, one after the other.