Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d.

(a) Find an expression for the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines. Use m for the mass, v for the speed and d for the distance of separation.

L = 2*m*v*(d/2) = m*v*d

To find the expression for the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines, we can start by defining the angular momentum for each individual particle.

The angular momentum (L1) of the first particle, traveling in one direction, around the midpoint between the two lines can be calculated using the formula:

L1 = m * v * r1

where m is the mass of the particle, v is its speed, and r1 is the distance between the midpoint and the first particle.

Similarly, the angular momentum (L2) of the second particle traveling in the opposite direction is given by:

L2 = m * v * r2

where r2 is the distance between the midpoint and the second particle.

Since the particles are traveling in opposite directions along parallel lines, the distance between them is equal to d.

The total angular momentum (L) of the two-particle system around the midpoint can be obtained by summing the angular momenta of the individual particles:

L = L1 + L2

Substituting the expressions for L1 and L2, we have:

L = m * v * r1 + m * v * r2

However, since the midpoint is equidistant from both particles, we have r1 = r2 = d/2. Substituting this into the equation, we get:

L = m * v * (d/2) + m * v * (d/2)
= m * v * d/2 + m * v * d/2
= m * v * d

Therefore, the expression for the magnitude L of the angular momentum of the two-particle system around a point midway between the two lines is L = m * v * d.