Simple mechanics

• Vector quantities have both a magnitude and a direction, while scalar quantities only have a magnitude.
• Vectors can be resolved by finding their vertical and horizontal components, and then adding them together, as vectors which are perpendicular do not affect each other.
• For an object to be in equilibrium, there must be no resultant force or moment acting on the object.
• The moment around a point can be found by multiplying the force by the perpendicular distance from the point to the line of action.
• A couple is a pair of coplanar forces where the two forces are equal in magnitude but opposite in direction.
• The centre of mass of an object is the point at which all the mass of an object can be presumed to act. If the object is uniform, this will be at the very centre of the object.
• In projectile motion, the projectile's horizontal and vertical components can be evaluated separately, with the acceleration of the horizontal velocity being zero and the acceleration of the vertical velocity being g.
• Free fall is where an object experiences an acceleration of g.
• Friction opposes the motion of the object, and so acts in the opposite direction to motion.
• Lift is an upwards force which acts on objects travelling in a fluid, is caused by the object creating a change in direction of fluid flow, and acts perpendicular to the direction of fluid flow.
• Terminal velocity occurs where frictional and driving forces acting on an object are equal.
• Newton's first law states that an object will remain travelling at a constant velocity until it experiences a resultant force.
• Newton's second law states that the force acting on an object is equal to the rate of change of momentum.
• Newton's third law states that for each force experienced by an object, the object exerts an equal and opposite force.
• Momentum is always conserved in an interaction, and can be found by multiplying mass by velocity.
• Impulse is the change in momentum, and can also be found by multiplying force by time or finding the area of a force-time graph.
• Cars have crumple zones, seat belts which stretch slightly and air bags, all which increase the impact time, therefore decreasing the forces on the passenger and reducing the risk of injury.
• In elastic collisions, momentum and kinetic energy are conserved and in inelastic collisions, only momentum is conserved. If two objects coalesce (join together) after the collision, then it is inelastic.
• Work done is the energy transferred by a force over a distance and can be found by multiplying the component of force in the direction of motion by distance.
• Power is the rate of energy transfer and equals work done divided by time, and therefore force multiplied by velocity, as velocity equals distance divided by time.
• Efficiency is the useful power output divided by the input power.
• The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or stored.
• Gravitational potential energy is mass multiplied by gravity multiplied by the change in height, and kinetic energy equals 1/2 multiplied by mass multiplied by velocity squared.