# A2 Physics-Further Mechanics

Main subtitles are points from the specification. Notes are taken from a variety of textbooks. Note: last point has no notes as all information just tells you the equations, which are fairly self explanatory

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• Created on: 10-06-12 10:51

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Unit 4-Physics On The Move
Topic 1-Further Mechanics
Use the expression p=mv
Momentum = mass x velocity: i.e. p=mv, units kg m s¹
Momentum is a vector quantity, with both magnitude and direction.
Investigate and apply the principle of conservation of linear
momentum to problems in one dimension
Conservation of linear momentum
The linear momentum of any closed system is conserved. Linear momentum is a vector quantity
and each component is conserved independently.
When two things interact, the force exerted on one is always equal and opposite to the force
exerted on the other (Newton's third law). The interaction time is the same for both so they receive
equal and opposite impulses. This means that impulses on two colliding objects have the same
magnitude but opposite directions, meaning that the change in momentum of the two bodies is also
equal in magnitude and opposite in direction. There is no change in the total linear momentum of the
system of the two objects. This is an example of a conservation law-the two cars have interacted but
the total linear momentum is the same before and after the collision. All interactions conserve linear
momentum, and all forces arise through interactions. So the total linear momentum of the universe is
constant. For practical purposes we apply the law in a more restricted way to closed systems.
Newton's third law of motion
Forces never arise singly but always in pairs as the result of interactions
When A interacts with B the force A exerts on B is always equal to the force B exerts on A
but in the opposite direction along the same line of action
Because these pairs of forces arise from an interaction they are always of the same type:
for example, both gravitational or both electromagnetic
Action-reaction pairs always act on different bodies, never on the same body
Investigate and relate net force to rate of change in momentum in
situations where mass is constant (Newton's second law of motion)
The second law of motion
The resultant force F exerted on a body is directly proportional to the rate of change of linear
momentum p of that body

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### Page 2

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Resultant force (N) is proportional to the rate of change of linear momentum (kg m s²), which is the
same as saying the resultant force is proportional to the final linear momentum minus the initial linear
momentum all divided by the time for which the force acts. Therefore, strictly speaking, F in the
equation is the average resultant force during time t. Momentum, force and velocity are all vectors,
so the momentum changes are parallel to the resultant applied forces.…read more

### Page 3

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Collisions in two dimensions
Many collisions and interactions occur in more than one dimension. Linear momentum is a vector
quantity, and so the vector sum of all momenta after a collision or interaction must equal the original
momentum vector. To solve problems in more than one dimension, it is best to resolve all momenta
along a carefully chosen set of axes and then conserve each component of momentum

### Page 4

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Angular displacement ()-The angle (in radians) turned through some time. = arcradius
length
. 2
Angular velocity ()-The rate of change of angular displacement (rad s¹). = t =
v
r
Explain the concept of angular velocity, and recognise and use the
relationships v=r and T= 2
Angular velocity and tangential velocity
When something moves in a circle, its instantaneous linear velocity is always parallel to a tangent to
the circle; this is called its tangential velocity. It has no radial velocity.…read more

### Page 5

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²
Use the expression for centripetal force F=ma= r and hence
derive and use the expressions for centripetal acceleration, a= v²
r