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Linear Momentum

The Impressive Impulse The impressive impulse This aggressive image shows an impressive punch at the opponent. Maximum power over a short period of time leaves a greater damage. What a boxer has to do if he or she has to sustain those punches? Lets learn more about Impulse and its implications, in this topic.

Learning Objectives

After completing the topic, the student will be able to:

  • Define, discuss, correlate and identify the center of mass of any given object.
  • Understand and identify the center of mass of a two-body system.
  • Analyze and detect the center of mass of rigid bodies.
  • Investigate and determine the motion of center of mass.
  • Define linear momentum and illustrate the conservation of linear momentum related to center of mass.
  • Distinguish and differentiate about the center of mass and center of gravity.
  • Evaluate the location of center of gravity.
  • Define, discuss and relate, equilibrium with general conditions and its different types.
  • Understand, analyze and apply, linear momentum to real world applications.
  • Define, understand, investigate and apply, impulse to daily life activities.
  • Understand the conservation of momentum and apply it to real world situations.
  • Understand the concept of collisions and its types. Also extend it to two dimensions to evaluate real world situations.
Conservation of momentum Conservation of momentum When a bullet is shot from a gun, the gun recoils, so that sum of bullet's momentum and the gun's momentum in the opposite direction, cancel out and the final momentum and initial momentum of the system is equalized.
Linear Momentum

If a ping pong ball and a football are rolling towards you at the same speed, you will notice that to bring them to a halt, you will have to apply larger force on the football. The ping pong ball stops easily. In another situation, if two footballs are moving towards you at different speeds, then you will notice that the football with the higher speed is more difficult to stop. It appears from these observations that the force applied (and time duration for which the force is applied) to bring about any change in motion, depends on both the mass and the velocity of the body. There is inertia of motion. A term momentum is used to describe this inertia or quantity of motion.

Momentum is denoted by p. Momentum is the product of mass (m) and velocity (v) of the moving body. It is a vector quantity and is written as

Momentum of a body     ------> (i)

Since m is a scalar and v is a vector quantity, momentum is a vector quantity. It has same direction as the velocity of a body.

The standard unit for measuring momentum is kg.m/s or kilogram–meter per second. We can see from the definition that a moving object can have a large momentum if either its mass or its velocity is large.

Relation between K.E and linear momentum

We know, K.E = 1/2 mv2 ------> (ii)
From (i) and (ii) we have
               K.E = p2/2m ------> (iii)

Linear momentum Linear momentum vector of a particle Linear momentum is a vector quantity. A particle's momentum has the same direction as its velocity.
Force and momentum

A train is harder to stop than a car moving at the same speed because the train has more momentum than the car. This is because of its greater mass. If we go back to the definition of force: F = m. a

Acceleration is rate of change of velocity Acceleration is rate of change of velocity

From combining all the three above equations, we can say that force is rate of change of momentum. Another term that is frequently used in equations of motion is impulse. Impulse is force multiplied by time. Impulse has the same units as momentum (newton – second or kilogram–meter per second), but there is a distinction: impulse is applied force at an instant of time. We will discuss about impulse a little later.

To fully describe the momentum of a 1 kg ball moving eastward at 5 m/s, you must give information about both the magnitude and the direction of the ball. It is not enough to say that the ball has 5 kg. m/s of momentum; the momentum of the ball is not fully described until information about its direction is given. The direction of the momentum vector is the same as the direction of the velocity of the ball.

If the ball is moving eastward, then its momentum can be fully described by saying that the ball has a momentum of 5 kg. m/s, directed eastward. From the definition of momentum, it becomes obvious that an object has a large momentum if either its mass or its velocity is large. Both variables are of equal importance in determining the momentum of an object. An object having zero velocity has zero momentum.

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