DYNAMICS

SCIENCE AND PHYSICS

► Dynamics is a branch of physics that examines the influences on the

motion of an object
 MASS AND WEIGHT
• Mass is a measure of the amount of matter in an object
• Consequently, this is the property of an object that resists change in motion
• The greater the mass of a body, the smaller the change produced by an applied force
• The SI unit for mass is the kilogram (kg)
Weight
● Weight is the effect of a gravitational field on a mass
● Since it is a force, it is measured in newtons (N) and is a vector quantity
● The weight of a body is equal to the product of its mass and the acceleration of
free fall Where:
○ W = weight in newtons (N)
○ m= mass in kilograms (kg)
○ g = acceleration of freefall in metres per second (m s-2)
● The acceleration of freefall, g, on Earth, is 9.81 m s-2
 MASS AND WEIGHT
Mass v weight
● An object’s mass always remains the same, however, its weight will differ
depending on the strength of the gravitational field at different locations
within the Universe
● For example, the gravitational field strength on the Moon is 1.63 N kg-1,
meaning an object’s weight will be about 6 times less than on Earth
 INERTIA
● Inertia is the tendency of an object to continue its state of rest or moving in a
straight line with constant velocity
● It is actually a measure of its mass
● More the mass more the inertia
● More the speed more the inertia
 INERTIA
● Inertia is the tendency of an object to continue its state of rest or moving in a
straight line with constant velocit
● It is actually a measure of its mass
● More the mass more the inertia
● More the speed more the inertia
MASS AND WEIGHT
 Newton's three laws of motion

Newton's first law

● Newton’s First Law of Motion states that:
A body will remain at rest or move with constant velocity unless acted on by a resultant force
● If the forces acting on an object are balanced, the object is said to be in equilibrium
○ There is no resultant force (the resultant force = 0)
○ There is no change in the object's motion
■ If the object was moving at a constant velocity, it will continue to move at that constant velocity
■ If the object was at rest, it will remain at rest
● If the forces acting on an object are not balanced:
○ There is a resultant force
○ There is a change in the object's motion
■ The object may speed up (acceleration)
■ The object may slow down (negative acceleration)
■ The object may change direction (a change in velocity, hence acceleration)
 Newton's three laws of motion

Newton's second law

● Newton's second law of motion describes the change in motion that occurs when the forces acting on an
object are not balanced
● Newton's second law can be stated as:
A resultant force acting on a body will cause a change in the object's motion in the direction of the force
● Newton's second law can also be stated in terms of momentum:
The rate of change in momentum is proportional to the magnitude of the force
● Newton's second law can also be written as:

● Where:
○ F = force in newtons (N)
○ m = mass in kilograms (kg)
○ a = acceleration in metres per second squared (m s-2)
■
 FORCE AND ACCELERATION

● Newton's second law of motion tells us that objects will accelerate if there is a resultant
force acting upon them
● This acceleration will be in the same direction as this resultant force

● Where:
○ F = force in newtons (N)
○ m = mass in kilograms (kg)
○ a = acceleration in metres per second squared (m s-2)

Resultant force
● Since force is a vector, every force on a body has a magnitude and direction
● The resultant force is therefore the vector sum of all the forces acting on the body
● The direction of the force is indicated as either positive or negative
 FORCE AND ACCELERATION

Acceleration
● Newton’s second law can be used to find the acceleration of an object of a known
mass
● Since acceleration is also a vector, it can be either positive or negative depending
on the direction of the resultant force
● An object will speed up (positive acceleration) if the resultant force acts in the
same direction as the direction of motion
● An object will slow down (negative acceleration) if the resultant force acts in the
opposite direction to the direction of motion
● The acceleration will always be in the same direction as the resultant force
FORCE AND ACCELERATION
FORCE AND ACCELERATION
 Linear momentum

● Linear momentum, p, is defined as the product of mass and velocity

● Where:
○ p = linear momentum in kilogram metres per second (kg m s-1)
○ m = mass in kilograms (kg)
○ v = velocity in metres per second (m s-1)
● Momentum is a vector quantity; it has both magnitude and direction
● It can have a positive or negative value which describes its direction in a one
dimensional plane
○ If an object travelling to the right has positive momentum, an object travelling to
the left (in the opposite direction) has a negative momentum
Linear momentum
 Newton's three laws of motion

Newton's second law

● Newton's second law can also be stated in terms of momentum:
The rate of change in momentum is proportional to the magnitude of the force
● Newton's second law can also be written as:

● Where:
○ F = force in newtons (N)
○ m = mass in kilograms (kg)
○ a = acceleration in metres per second squared (m s-2)
■
 Force & momentum

Newton's second law

● Newton's second law can also be stated in terms of momentum:
The rate of change in momentum is proportional to the magnitude of the force
●
● Where:
○ F = force in newtons (N)
○ p = momentum in kilogram metres per second (kg m s-1)
○ t = time in seconds (s)
○ Δ (the Greek letter delta) = change in
● Change in momentum, Δp, can also be expressed as:
change in momentum = final momentum − initial momentum

● Force and momentum are vector quantities

○ They can have a positive or negative direction
https://drive.google.com/drive/folder
s/1mEH9aHsTKJDC06LmjEBLld5q
Force & momentum
12B4_TmX?usp=drive_link

Direction of forces
● The force that is equal to the rate of change of momentum is still the resultant force
● The force on an object will be negative if the direction of the force opposes the direction of its
initial velocity
● This means that a force is exerted by the object it has collided with
 Force & momentum

Time of impact
● The force exerted is also determined by the time taken for the impact to occur
● The same change in momentum, over a longer period of time will exert less force, and vice
versa
○ As Δt increases, F decreases, when Δp remains the same
○ As Δt decreases, F increases, when Δp remains the same
For
Force & momentum
 Newton's three laws of motion
Newton's third law
● Newton’s third law of Motion describes the force interaction between two different objects
Whenever two bodies interact, the forces they exert on each other are equal and opposite
● If body A exerts a force on body B, then body B will exert a force on body A of equal
magnitude but in the opposite direction
● Therefore, forces always occur in pairs
● A Newton's third law force pair must be:
○ the same type of force
○ the same magnitude
○ opposite in direction
○ acting on different objects
Non uniform motion
 Drag forces
● Drag forces are forces acting in the opposite direction to an object moving through a fluid (either gas or liquid)
● Examples of drag forces are friction and air resistance
● A key component of drag forces is that the magnitude of the drag force increases with the speed of the object
○ As an object speeds up, the drag force increases
○ As an object slows down, the drag force decreases.
● Therefore, drag forces have the greatest effect at high speeds
● Consider a car traveling forward on a straight road
● When the car is accelerating:
○ The driving force is greater than the frictional force
○ The resultant force is acting in the same direction as the direction of motion
○ Therefore, the car speeds up
● When the car is traveling at a constant velocity:
○ The driving force is equal to the frictional force
○ There is no resultant force acting on the car
○ Therefore, the motion of the car remains the same (continues traveling at a constant velocity)
● When the car is decelerating:
○ The driving force is less than the frictional force
○ The resultant force is acting in the direction that opposes the motion of the car
○ Therefore, the car slows down
Drag forces
 Air resistance
● Air resistance is an example of a drag force
● Objects experience friction when moving through the air as they collide with the
air particles.
● Air resistance depends on the shape of the object and the speed at which it is
travelling
● Since drag force increases with speed, air resistance becomes important when
objects move faster
 Terminal velocity
Terminal velocity
● For a body in free fall with no effects of air resistance (for example, on the moon), the
only force acting on it is weight
○ The resultant force is equal to weight
○ Therefore, the body accelerates at g, acceleration of free fall
● For a body in free fall, when air resistance is a factor (for example on Earth):
○ Weight is greater than air resistance, so the resultant force is in the direction of
motion
○ The body accelerates according to Newton's second law, F = ma
○ As the velocity increases, the drag force increases
○ The resultant force decreases, therefore the acceleration decreases
○ When the drag force equals weight, the resultant force is zero
○ The body falls at a constant velocity called terminal velocity
○ Terminal velocity is the maximum velocity the body can reach
https://www.geogebra.org/m/cqmxbk2v
 Air resistance
Falling objects with air resistance
● When objects fall through a fluid, the fluid exerts a frictional force on the object as it falls
○ Fluids are liquids or gases
● Frictional forces oppose the motion of an object
○ They act to slow it down
● When an object falls through air, it experiences air resistance
● Air resistance occurs as the object moving through the air collides with the air particles
● Air resistance increases as the speed of the object increases
● When objects fall through air, two forces are exerted on the object:
○ The force of weight
○ The force of air resistance
● When the force of air resistance becomes equal to the force of weight, then the object
stops accelerating and falls at a constant speed
○ This constant speed is called terminal velocity
https://pastpapers.papacambridge.com/viewer/caie/as-and-a-level-physics-9702-2012-nov-9702-w12-qp-21-pdf

https://phet.colorado.edu/sims/html/friction/latest/friction_all.html
 Linear momentum

● Linear momentum, p, is defined as the product of mass and velocity

● Where:
○ p = linear momentum in kilogram metres per second (kg m s-1)
○ m = mass in kilograms (kg)
○ v = velocity in metres per second (m s-1)
● Momentum is a vector quantity; it has both magnitude and direction
● It can have a positive or negative value which describes its direction in a one
dimensional plane
○ If an object travelling to the right has positive momentum, an object travelling to
the left (in the opposite direction) has a negative momentum
Linear momentum
 Linear momentum

● Linear momentum, p, is defined as the product of mass and velocity

● Where:
○ p = linear momentum in kilogram metres per second (kg m s-1)
○ m = mass in kilograms (kg)
○ v = velocity in metres per second (m s-1)
● Momentum is a vector quantity; it has both magnitude and direction
● It can have a positive or negative value which describes its direction in a one
dimensional plane
○ If an object travelling to the right has positive momentum, an object travelling to
the left (in the opposite direction) has a negative momentum
 Linear momentum
The principle of conservation of momentum
● The principle of conservation of linear momentum states that:
The total linear momentum before a collision is equal to the total linear momentum after a
collision unless the system is acted on by a resultant external force
● Therefore:
momentum before = momentum after
● Momentum is a vector quantity, therefore:
○ opposing vectors can cancel each other out, resulting in a net momentum of zero
○ an object that collides with another object and rebounds, has a positive velocity before the
collision and a negative velocity after
● Momentum is always conserved
Linear momentum
 Linear momentum
External and internal forces
● External forces are forces that act on a structure from outside e.g. friction and weight
● Internal forces are forces exchanged by the particles in the system e.g. tension in a string
○ Which forces are internal or external will depend on the system itself
● A system with no external forces acting can be described as a closed or isolated system
 Linear momentum
One-dimensional momentum problems
● Recall that linear momentum is p = mv
● Using the conversation of linear momentum, it is possible to calculate missing velocities and masses of
components in a system
● Elastic collisions are commonly those where objects colliding do not stick together and then move in
opposite directions
● Inelastic collisions are where objects collide and stick together after the collision
● To find out whether a collision is elastic or inelastic, compare the amount of kinetic energy in the system
before and after the collision
○ If the kinetic energy is conserved, it is an elastic collision
○ If the kinetic energy is not conserved, it is an inelastic collision
 Linear momentum
Elastic collisions
● When two objects collide, they may spring apart retaining all of the kinetic energy of the system
● This would be a perfect elastic collision
● In an elastic collision, all of the kinetic energy is conserved
● Recall the kinetic energy equation:
● Where:

○ Ek = kinetic energy in joules (J)

○ m = mass in kilograms (kg)
○ v = velocity in metres per second (m s-1)
● Kinetic energy depends on the speed of an object
● In a perfectly elastic collision (such as a head-on collision):
the relative speed of approach = the relative speed of separation
 Linear momentum
Coefficient of restitution
 Linear momentum
Inelastic collisions
● Whilst the momentum of a system is always conserved in interactions between objects, kinetic energy is not
always conserved
● An inelastic collision is one where kinetic energy is not conserved
● The kinetic energy is transferred to other energy stores
● Inelastic collisions occur when two objects collide and they crumple and deform
● All of the kinetic energy of the system may be transferred away from the system and the objects will come
to a halt
● Or some of the kinetic energy of the system may be transferred away and the objects will move as one body
at a slower speed than the original objects
● A perfectly inelastic collision is when two objects stick together after collision
Linear momentum
Linear momentum
Linear momentum
Linear momentum-GRAPH
 Linear momentum

Two-dimensional momentum problems

● We know that momentum is always conserved
● This doesn't just apply to the motion of colliding objects in one dimension (in one line),
but this is true in every direction
● Since momentum is a vector, it can be split into its horizontal and vertical component
a. This is done by resolving vectors
 ● Consider again the two colliding balls A and B

● This time, they move off in different

directions,
so we now need to consider their
momentum in the x direction and
separately, their momentum in the y
direction
○ This is done by resolving the
velocity vector of each ball after
the collision
A snooker ball of mass 0.15 kg collides with a stationary snooker ball of mass 0.35 kg. After the
collision, the second snooker ball moves away with a speed of 0.48 m s–1. The paths of the balls
make angles of 43° and 47° with the original direction of the first snooker ball.Calculate the speed u1
and v1 of the first snooker ball before and after the collision.
ctice Past Year Questions
MJ12 P11 Q11 (pg11) Elastic collision statement
MJ12 P12 Q12 (pg11) Relative Velocity
ON12 P11 Q12 (pg12) Relative speeds choice
ON12 P11 Q14 (pg12) Lead pellet Clay block
ON12 P12 Q12 (pg12) Ball thrown against wall
ON12 P12 Q13 (pg13) Elastic Collision
ON12 P13 Q11 (pg13) Relative speeds choice
ON12 P13 Q12 (pg13) changes in p and v
MJ13 P11 Q10 (pg14) Conservation Statement
MJ13 P11 Q11 (pg14) Collision KE
MJ12 P13 Q10 (pg14) Nuclear Decay
MJ13 P13 Q11 (pg15) Relative speeds choice
ON13 P13 Q10 (pg15) Moving Thorium
ON13 P13 Q11(pg15) momentum KE compare
ON13 P13 Q13 (pg15) pellet on wooden block
MJ14 P11 Q9 (pg15) Collision KE
MJ14 P12 Q7 (pg16) Colliding Train
MJ14 P13 Q12 (pg17) Explosion
ON14 P11 Q7 (pg17) Conservation statement
ON14 P11 Q9 (pg17) Railway trucks
MJ15 P11 Q11 (pg18) mass hits a wall
ements
MJ16 P11 Q10 (pg20) Relative Velocity
MJ16 P12 Q9 (pg21) Possible values of p1 and p2
MJ17 P12 Q7 (pg25) Rubber ball Bounce
MJ17 P12 Q8 (pg26) Golf Ball momentum change
ON17 P11 Q10 (pg26) Principle of Conservation
ON17 P11 Q11 (pg26) Relative Speed
ON17 P12 Q9 (pg27) Slow vehicle, fast vehicle
FM18 P12 Q10 (pg27) Steel pellet average force
MJ18 P11 Q9 (pg27) Head-on elastic collision
MJ18 P12 Q8 (pg27) Average Force on the wall
ON18 P12 Q9 (pg29) Collision statement
ON18 P12 Q10 (pg29) Spheres XY
ON18 P13 Q7 (pg29) Isolated Sphere acceleration
FM19 P12 Q8 (pg30) Direction of ball X
FM19 P12 Q10 (pg30) Loss of KE in collision
MJ19 P11 Q11 (pg31) Collision of Helium atom
MJ19 P12 Q11 (pg31) Magnets P and Q
ON19 P11 Q10 (pg32) Glider P Q
ON19 P13 Q9 (pg33) Colliding relative speeds
FM20 P12 Q10 (pg34) Ball PQ Collision statement
MJ20 P11 Q10 (pg35) Stationary Toy Gun Fire
MJ20 P12 Q9 (pg35) Incorrect equation collision
MJ20 P13 Q10 (pg35) Fraction of initial KE
ON20 P11 Q10 (pg36) 2 trolleys KE lost
ON20 P11 Q9 (pg36) Rock R Comet
ON20 P12 Q10 (pg37) Before vs after collision
ON20 P12 Q11 (pg37) Pellet vs block M
ON20 P13 Q10 (pg37) 5m collision