• Linear momentum,?p, is defined as the product of mass and velocity

• Momentum is a?vector?quantity - it has both a?magnitude?and a?direction
• This means it can have a negative or a positive value
  • If an object travelling to the?right?has?positive?momentum, an object travelling to the?left?(in the opposite direction) has a?negative?momentum
  • The negative or positive directions are?defined by the observer?on a case-by-case basis
• The SI unit for momentum is?kg m s^?1

Direction of Momentum

• If a ball of mass 60 g travels at 2 m s^?1, it will have a momentum of 0.12 kg m s^?1
• If it then hits a wall and rebounds in the exact opposite direction, it will have a momentum of ?0.12 kg m s^?1

When the ball is travelling in the opposite direction, its velocity is negative.?Since momentum = mass × velocity, its momentum is also negative

• Both the tennis ball and the brick have the?same momentum
• Even though the brick is much?heavier?than the ball, the ball is travelling much?faster?than the brick
• This means that on impact, they would both exert a?similar force?(depending on the time it takes for each to come to rest)

Force & Momentum

• Force is defined as the?rate of change of momentum?on a body
• The change in momentum is defined as the final momentum minus the initial momentum
• These can be expressed as follows:

• It should be noted that the force in this situation is equivalent to Newton's second law:

F = m × a

• Only when mass is constant
  • In situations where?mass?is?not constant, Newton's second law can?only?be considered to?assist descriptions?and not for calculations

• The force and momentum equation can be derived from Newton's Second law and the definition of acceleration

Direction of Forces

• Force and momentum are?vectors?so they can take either positive or negative values
• The force that is equal to the rate of change of momentum is still the?resultant force
• A force on an object will be negative if it is directed in the opposite motion to its initial velocity
  • This means that the force is?produced by the object it has collided with

The wall produces a force of -300N on the car and (due to Newton’s Third Law) the car also produces a force of 300 N back onto the wall