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Vectors
any physical quantity that has a direction, as well as a magnitude
Represented with a line and an arrow
Length of line indicates magnitude
Arrow indicates direction
Scalar
quantity which only has magnitude
Represented using a line
Length of line indicates magnitude
Rules for adding vectors
Vectors in same direction have the magnitudes added together
Vectors in opposite directions have the magnitudes subtracted
If the object does not move, no work is done
Work done must be in same direction as the force
Equilibrium
no net force or moment (resultant force) acts on it
Forces and moments are balanced
resultant force = 0
Equilibrant vector
resultant vector in opposite direction
For a system to be in equilibrium
Sum of x components = 0
Sum of vertical components or forces = 0
Torque
moment of a force
Centre of gravity
where the entire weight of the object seems to act
Point through which a single force has no turning effect on the body
Centre of mass
where the entire mass of an object seems to be concentrated
Point through which a single force has no turning effect on the body
Uniform - evenly distributed
In uniform gravitational field the centre of mass is the same place as the centre of gravity
Located at the point of symmetry in symmetrical objects with uniform density
Principle of moments (for a body in equilibrium)
Total clockwise moment = total anticlockwise moment
Stability
An object is stable when its centre of mass lies above its base
The wider base an object has, the lower its centre of mass and it is more stable
The narrower base an object has, the higher its centre of mass and the object is more likely to topple over if pushed