# Mechanics

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Key words

• String- Inextensible and has no mass
• Particle- Has no size but does have mass
• Rigid Body- Has size but does not change shape
• Smooth- Has no friction
• Rough- Has friction
• Light- Has no mass
• Inelastic/Inextensible- Does not stretch

Kinemetics in one dimension

• In a Displacement-time graph, the velocity is calculated by working out the gradient  (y/x =velocity)
• Velocity-time graphs have a gradient equivalent to acceleration. (y/x=accelration)
• Area under a Velocity-time graph= Distance travelled
• v=u+at
• s=((u+v)t)/2
• v^2=u^2+2as
• s=ut+0.5at^2 or s=vt-0.5at^2
•  Where s=displacement, u=initial velocity, v=final velocity, a=acceleration, t=time.
• Formulae only work when acceleration is constant
• Acceleration due to gravity(g)= 9.8 metres per second

Kinematics in two dimensions

• Positions, velocities and accelerations can be expressed in the form xi+yj
• Constant acceleration equations (shown above) can be used in two dimensions. Once in the i direction and once in the j direction. Adding both i and j together gives a vector.
• Magnitude and Direction of vectors can be calculated using trigonometry and pythagoras.

Forces

• Force is a vector quantity
• Resultant force=two or more forces added together using its perpendicular components.
• Particle is in equilibrium if resultant=0
• Weight= mass x acceleration due to gravity (W=mg)
• Frictional force between two surfaces in contact will act in a opposite direction to the