CENTRE OF MASS, LINEAR MOMENTUM AND IMPULSE.

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Here we are going to have a look on important topics of mechanics. We start with centre of mass. As we all know every matter has mass and gravity acts on them. Then we assume that gravitational force acts on a point of body at which all mass of body has concentrated. In real that is not the case but for sake of problems we consider like that. So this point at which mass is concentrated is called centre of mass. If there are more than one bodies, then we need to find out centre of these bodies. For this, we need to take one reference point as origin. Then there are formulas to calculate x, y and z coordinate of centre of mass of given system. For continuous bodies, we sum up product in formula by using integration. If some external force acts on any one of body in system, then centre of mass also moves along it. This can be studied under motion of centre of mass. But if internal forces cause the motion of particles then, centre of mass follows same path as before or remains same.

Generally linear momentum is defined as total mass of system multiplied by velocity of centre of mass. Linear momentum remains conserved if external force on system is zero. This helps us in solving problems related to internal forces. Also rate of change of momentum is external force. It is a vector quantity and has specific direction. Now when we apply force on given system suddenly (in short time), we call it as impulse. It is force multiplied by time for which it’s applied and also change in momentum before and after impact. These two equations are enough to solve problem on impulse.

Typical mistakes:

  1. While finding centre of mass, many make mistake in sign of distances of mass from reference origin.
  2. While doing integration, choose small element such that it will cover all points upon integration.
  3. Sign of linear momentum depends on direction of velocity and our reference, so don’t confuse in it.
  4. First find whether motion is caused by internal or external force.

Tips/guidelines:

  1. Not in all problems you need to do calculations for finding centre of mass, many can be found by observation like in similarity cases.
  2. Try to find centre of mass for continuous bodies by integration as its more important and somewhat tough.
  3. Conservation of linear momentum gives equations while solving system. So don’t miss them.
  4. Linear momentum is used in problems of collision, explosion of particles.
  5. Solve typical type of problems for impulse.

Summary:

This covers basic concepts which can be used in solving complicated problems of mechanics. Practice problems of collision, explosion in air while moving and also problems on bullets which involve impulse concept. Focus mainly on linearly momentum here.

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