Oblique impact between two spheres

Section 1: Understanding Oblique Impact

Grasp the concept of oblique impact, which occurs when two spheres collide at any angle other than head-on.
Master the theory of the law of Conservation of Linear Momentum, which states that the total linear momentum of two colliding objects is conserved, provided there are no external forces.
The linear momentum before the collision is equal to the linear momentum after the collision, or mathematically expressed: m1u1 + m2u2 = m1v1 + m2v2 where ‘m’ represents mass, ‘u’ the velocity before impact and ‘v’ the velocity after impact.

Section 2: Laws of Oblique Impact of Spheres

Understand the concept of coefficient of restitution ‘e’ which demonstrates the relationship between the velocities of two spheres before and after impact. ‘e’ is defined as the ratio of the separation speed (speed after impact) to the approach speed (speed before impact).
The coefficient of restitution can be given as: e = (v2 - v1) / (u1 - u2).
Distinguish between elastic and inelastic collisions. In an elastic collision, ‘e’ equals 1 meaning kinetic energy is conserved, while in inelastic collisions, ‘e’ is less than 1 indicating some loss of kinetic energy.

Section 3: Calculating velocities after impact

Be aware of the two essential steps in calculating velocities after an oblique impact. The first step is to resolve the velocities into components: along the line of impact (tangential component) and perpendicular to the line of impact (normal component).
Recognize that only the normal components change after the collision. The tangential components remain unaffected.
After the collision, the normal components can be calculated using the laws of conservation of linear momentum and the coefficient of restitution.

Section 4: Problem-Solving Strategies

When solving problems, first sketch a diagram of the collision showing the directions of motion and their components.
Solve the equations of linear momentum and restitution simultaneously to find the post-collision velocities.
Consistently check all units of measurements are in order. Normally, mass is in kilograms and velocity is in metres per second.
Engage in regular practice problems to get a thorough understanding of oblique impact between spheres.