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Two particles of masses m1 and m2 are moving in a straight line with velocities

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Question: Two particles of masses m1 and m2 are moving in a straight line with velocities v1 and v2 respectively. If they collide elastically, what is the expression for the change in angular momentum about the center of mass?

Options:

  1. m1v1 + m2v2
  2. m1v1 - m2v2
  3. 0
  4. m1v1 + m2v2 - (m1v1\' + m2v2\')

Correct Answer: m1v1 + m2v2 - (m1v1\' + m2v2\')

Solution: 

In an elastic collision, the total angular momentum about the center of mass is conserved.

Two particles of masses m1 and m2 are moving in a straight line with velocities

Practice Questions

Q1
Two particles of masses m1 and m2 are moving in a straight line with velocities v1 and v2 respectively. If they collide elastically, what is the expression for the change in angular momentum about the center of mass?
  1. m1v1 + m2v2
  2. m1v1 - m2v2
  3. 0
  4. m1v1 + m2v2 - (m1v1' + m2v2')

Questions & Step-by-Step Solutions

Two particles of masses m1 and m2 are moving in a straight line with velocities v1 and v2 respectively. If they collide elastically, what is the expression for the change in angular momentum about the center of mass?
  • Step 1: Understand that angular momentum is a measure of the rotational motion of an object around a point, in this case, the center of mass.
  • Step 2: Recall that in an elastic collision, both momentum and kinetic energy are conserved.
  • Step 3: Identify the center of mass (CM) of the two particles. The position of the CM can be calculated using the formula: CM = (m1 * x1 + m2 * x2) / (m1 + m2), where x1 and x2 are the positions of the particles.
  • Step 4: Calculate the initial angular momentum about the center of mass before the collision using the formula: L_initial = m1 * v1 * r1 + m2 * v2 * r2, where r1 and r2 are the distances from the center of mass to each particle.
  • Step 5: After the collision, calculate the final angular momentum using the new velocities of the particles, which can be found using the conservation of momentum and kinetic energy.
  • Step 6: The change in angular momentum is found by subtracting the initial angular momentum from the final angular momentum: Change in L = L_final - L_initial.
  • Step 7: Since angular momentum is conserved in an elastic collision, the change in angular momentum about the center of mass is zero.
  • Elastic Collision – An elastic collision is one in which both momentum and kinetic energy are conserved.
  • Angular Momentum – Angular momentum is the rotational equivalent of linear momentum and is calculated as the product of the moment of inertia and angular velocity.
  • Center of Mass – The center of mass is the point at which the mass of a system is concentrated and about which the system's mass is evenly distributed.
  • Conservation Laws – In isolated systems, certain quantities such as momentum and angular momentum remain constant before and after collisions.
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