is a fundamental concept in physics, describing an object's motion based on its mass and velocity. It's crucial for understanding collisions, explosions, and the effects of forces on moving objects.
differs from in its vector nature and linear relationship with velocity. The principle is key to analyzing interactions between objects, from simple collisions to complex systems like rockets and explosions.
Linear Momentum
Calculation of momentum
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Calculate momentum by multiplying an object's mass and velocity
Use the formula [p = mv](https://www.fiveableKeyTerm:p_=_mv) where p represents momentum (), m represents mass (kg), and v represents velocity (m/s)
Momentum is a , meaning it has both magnitude and direction
Direction of momentum aligns with the direction of velocity
Express momentum in various units
SI units for momentum are kilogram-meter per second (kg⋅m/s)
English system units for momentum are slug-foot per second ()
Examples:
A 1,000 kg car traveling at 20 m/s has a momentum of 20,000 kg⋅m/s
A 0.145 kg baseball pitched at 40 m/s has a momentum of 5.8 kg⋅m/s
Momentum vs kinetic energy
Understand the differences between momentum and kinetic energy in representing motion
Momentum is a vector quantity (has magnitude and direction) while kinetic energy is a scalar quantity (has only magnitude)
Momentum is linearly proportional to velocity (p=mv) while kinetic energy is proportional to the square of velocity (KE=21mv2)
Momentum is always conserved in closed systems (elastic and inelastic collisions) while kinetic energy is only conserved in elastic collisions
The determines the elasticity of a collision
Compare the formulas for momentum and kinetic energy
Momentum: p=mv
Kinetic energy: KE=21mv2
Examples:
A 2 kg object moving at 3 m/s has a momentum of 6 kg⋅m/s and a kinetic energy of 9 J
Doubling the velocity of an object doubles its momentum but quadruples its kinetic energy
Conservation of linear momentum
Apply the to collisions and explosions
In a , total momentum before an interaction equals total momentum after the interaction
Use the formula m1v1+m2v2=m1v1′+m2v2′ where v1 and v2 are initial velocities and v1′ and v2′ are final velocities
Distinguish between elastic and inelastic collisions
Elastic collisions conserve both kinetic energy and momentum (colliding billiard balls, certain atomic and subatomic particle interactions)
Inelastic collisions conserve momentum but not kinetic energy, converting some kinetic energy into other forms like heat or sound (colliding vehicles, a ball of clay hitting a wall)
Analyze the conservation of momentum in explosions
Initial momentum of the system is zero before the
After the explosion, the sum of the momenta of all fragments equals zero
Examples:
In a head-on between two objects of equal mass, they will bounce off each other with the same speed but opposite directions
When a firecracker explodes, the fragments fly off in different directions, but the vector sum of their momenta is zero
Impulse and Newton's Second Law
Understand as the change in momentum
is equal to the force applied multiplied by the time interval of application
Impulse is directly related to of Motion
Apply Newton's Second Law to momentum problems
The law states that the rate of change of momentum is equal to the applied force
This relationship is crucial in understanding how forces affect the motion of objects
Analyze the concept of in multi-particle systems
The is the point where the entire mass of a system can be considered concentrated
It's important in calculating the overall motion of complex objects or systems
Explore the phenomenon of in various scenarios
Recoil occurs due to conservation of momentum when a part of a system is ejected
Examples include the kickback of a gun or the thrust of a rocket