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Paper 4 Further Mechanics
Momentum is a measure of an accelerating force over a period of time. It is measured by the product of mass and velocity.
p = mv (kg ms-1)
Momentum is a vector quantity, as it also indicates direction. The definition of momentum also shows that:
To accelerate an object we need to give it momentum. This is done be applying a force over a time, t.
impulse = F t = p
The principle of conservation of momentum can be used to predict the motion of objects after a collision. It states that the sum of the total momenta before a collision will equal the some afterwards. This is
provided no external force acts upon the objects in the collision. When calculating the sum of momenta, the direction it applies must be considered and must be considered by making their magnitude negative if in
If an object explodes the sum of the momentum of the all momentum must equal 0, accounting for the direction of motion due to the laws of conservation of momentum.
When objects move in different directions, their momentum must be resolved into perpendicular components. Momenta sums can be carried out for the component directions.
In an elastic collision both momentum and kinetic energy are conserved. This means that the sum of momenta before equals the sum after i.e.
mAuA + mBuB = mAvB + mBvB
In an inelastic collision kinetic energy is not conserved, and momentum is lost through deformation of an object and heat and sound energy.
Angular displacement is the vector quantity representing by how much an object has turned. Angular velocity is the rate at which it does this.
t = T
If f = 1 , then
If we picture an object moving in a circle, it will have an instantaneous velocity (linear) in a given direction. As v = ts , and s is the arc length ( r) , then:
v = rt
As = ,
v = r
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Because the object is traveling in a circle, its velocity is constantly changing. This means is it accelerating. According to Newton's first law, for an object to accelerate, it must have a resultant force applied to it. This
resultant force is known as centripetal force.
F = mvr
As we know v = r ,
F = mr2
As F = ma , then formulas for angular acceleration can be derived.…read more