Lesson 20: Summary on Impulse and Linear momentum
- Momentum is a fundamental concept in physics that describes the effort required to set a body in motion or to stop it.
- It is a vector quantity defined as the product of an object’s mass and velocity (P = mv).
- The momentum of an object is directly proportional to both its mass and velocity.
- Therefore, a heavier or faster-moving object has greater momentum, making it harder to stop.
- The SI unit of momentum is kg m/s, and its direction is the same as the direction of the velocity vector.
- Changing an object’s momentum requires the application of a force, as described by Newton’s second law of motion.
- Impulse is the product of force and the time interval during which the force is applied (J = FΔt).
- It is a measure of the change in momentum of an object.
- Impulse is also a vector quantity and is measured in Newton seconds (Ns) or kg m/s.
- The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it.
- This concept is crucial for understanding the effects of forces acting over time, such as in car crashes where the impulse of the collision determines the impact severity on the occupants.
- The law of conservation of linear momentum states that when no external force acts on a system of interacting particles, the total linear momentum of the system is conserved.
- This principle applies to all types of collisions, both elastic and inelastic, and is not affected by changes in temperature, pressure, or other external conditions.
- In a collision, the momentum of individual particles may change, but the total momentum of the system remains constant.
- This law is fundamental in analyzing the behavior of colliding bodies.
- Collisions can be classified into elastic and inelastic collisions based on the conservation of kinetic energy.
- In an elastic collision, both kinetic energy and momentum are conserved.
- Elastic collisions are common among atomic and subatomic particles.
- In inelastic collisions, momentum is conserved, but kinetic energy is not.
- When colliding objects stick together after the collision, it is termed a perfectly inelastic collision.
- The lost kinetic energy in inelastic collisions is transformed into other forms of energy such as heat or sound.
- In an elastic collision, the total momentum and total kinetic energy of the system are conserved.
- The velocities of the colliding bodies after the collision can be determined using the conservation equations.
- For two bodies with masses m1 and m2 and initial velocities u1 and u2, the final velocities v1 and v2 can be calculated using the conservation of momentum and kinetic energy principles.
- In elastic collisions, the bodies often exchange velocities if they have equal masses.
- The center of mass is a crucial concept that simplifies the analysis of motion in a system of particles.
- It is the point where the total mass of the system is assumed to be concentrated.
- The motion of the center of mass is governed by Newton’s second law, and it moves as if all external forces act at this point.
- For a system of particles with masses m1, m2, …, and coordinates (x1, y1), (x2, y2), …, the center of mass coordinates (x_cm, y_cm) are calculated as weighted averages of the individual coordinates.
- The center of mass helps in understanding the overall motion of complex systems.