Maths Mechanics
ASSUME g = 9.8
Forces
Newton’s 2nd law: the resultant force on an object in a given direction equals the mass of
that object multiplied by the acceleration of that object in that direction
Use the following notation:
Newton’s 3rd law: if object A exerts a force on object B then object B will exert a force on
object A which is equal in magnitude and opposite in direction
If there is a resultant force on an object, it is accelerating in that direction, not necessarily
moving in that direction
Free body force diagram example:
Weight = the force acting on an object due to gravity
Reaction force = the force acting opposite and equally to another force as shown in NIII
Tension = the pulling force transmitted by the means of some one-dimensional continuous
object
o DO NOT NEED TO DOUBLE FOR TOTAL TENSION
You can group masses and forces if bodies within a system are not accelerating with respect
to each other
o Can combine internal forces where the NIII law pair are within the system
Cables and strings CANNOT be in thrust as they would just collapse in on themselves- must
be in tension
Rods can be in tension or thrust
Pulleys
Important Words
o Light -> string has no weight to account for so tension is the same everywhere
o Inextensible -> acceleration on one mass is equal and opposite to the acceleration
on the other mass
o Smooth -> if the pulley is rough then tension will not be equal throughout the string
o Taught -> if the string wasn’t taught, there wouldn’t be any tension
,SUVAT
For graphs, if there is an immediate drop or increase, draw a dotted line to connect
Friction
An object is in limiting equilibrium when the maximum amount of force is being applied
without the object moving and frictional force is at its maximum
o Object at the point of sliding/moving
F max=μR at limiting equilibrium or sliding (for static objects, F max ≤ μR )
o F max= maximum frictional force
o μ = coefficient of friction
o R = reaction force (take all forces in the direction of the surface into account
including components, not just weight)
Two objects of different masses can still have the same frictional force as μ may vary
between surfaces
Cannot have negative acceleration when working with friction as this means the friction
swaps direction
, Projectiles
Work out horizontal and vertical suvat and work from there
When throwing a projectile on Earth, horizontal acceleration is 0 and vertical will be -9.8
from upwards direction
Can split up any forces into horizontal and vertical components as they are like vectors
Be careful when splitting into components as DISTANCE can also be split
Equation of trajectory means writing the y distance travelled in terms of the x distance like a
line equation
ASSUME g = 9.8
Forces
Newton’s 2nd law: the resultant force on an object in a given direction equals the mass of
that object multiplied by the acceleration of that object in that direction
Use the following notation:
Newton’s 3rd law: if object A exerts a force on object B then object B will exert a force on
object A which is equal in magnitude and opposite in direction
If there is a resultant force on an object, it is accelerating in that direction, not necessarily
moving in that direction
Free body force diagram example:
Weight = the force acting on an object due to gravity
Reaction force = the force acting opposite and equally to another force as shown in NIII
Tension = the pulling force transmitted by the means of some one-dimensional continuous
object
o DO NOT NEED TO DOUBLE FOR TOTAL TENSION
You can group masses and forces if bodies within a system are not accelerating with respect
to each other
o Can combine internal forces where the NIII law pair are within the system
Cables and strings CANNOT be in thrust as they would just collapse in on themselves- must
be in tension
Rods can be in tension or thrust
Pulleys
Important Words
o Light -> string has no weight to account for so tension is the same everywhere
o Inextensible -> acceleration on one mass is equal and opposite to the acceleration
on the other mass
o Smooth -> if the pulley is rough then tension will not be equal throughout the string
o Taught -> if the string wasn’t taught, there wouldn’t be any tension
,SUVAT
For graphs, if there is an immediate drop or increase, draw a dotted line to connect
Friction
An object is in limiting equilibrium when the maximum amount of force is being applied
without the object moving and frictional force is at its maximum
o Object at the point of sliding/moving
F max=μR at limiting equilibrium or sliding (for static objects, F max ≤ μR )
o F max= maximum frictional force
o μ = coefficient of friction
o R = reaction force (take all forces in the direction of the surface into account
including components, not just weight)
Two objects of different masses can still have the same frictional force as μ may vary
between surfaces
Cannot have negative acceleration when working with friction as this means the friction
swaps direction
, Projectiles
Work out horizontal and vertical suvat and work from there
When throwing a projectile on Earth, horizontal acceleration is 0 and vertical will be -9.8
from upwards direction
Can split up any forces into horizontal and vertical components as they are like vectors
Be careful when splitting into components as DISTANCE can also be split
Equation of trajectory means writing the y distance travelled in terms of the x distance like a
line equation
