Dynamics
dynamics is the study of the forces causing
motion using words, diagrams, equations and graphs
forces cause
motion
Dr M
M. Marais
Last update 02/04/25
learning outcomes
•
understand Newton’s three laws of motion
•
explain the effect of forces on motion
•
identify and explain the difference between static and dynamic equilibrium
•
identify types of forces
•
construct free body diagrams
•
translate information about forces between words, pictures, equations and graphs
•
apply laws of motion to solving different problems
•
apply laws of motion to free fall and terminal velocity
laws of motion
Newton’s 1st law of motion (NI)
A body will remain in a state of rest,
or, uniform speed in a straight line,
unless it is acted upon by an external,
unbalanced force.
“Every body perseveres in its state of being at rest or of moving uniformly
straight forward, except insofar as it is compelled to change its state by the
forces impressed.”
https://www.scientificamerican.com/article/mistranslation-of-newtons-first-law-discovered-after-nearly-300-years1/
laws of motion
Newton’s 2nd law of motion (NII)
The change of motion (acceleration) of a
body is proportional to the force exerted
on it, and inversely proportional its mass.
a
a
Force
1
𝑚𝑎𝑠𝑠
a=k
𝐹
𝑚
𝐹
a=
𝑚
F = ma
“The change of motion of an object is proportional to the force impressed; and is
made in the direction of the straight line in which the force is impressed.” [14]: 114
https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#cite_note-:0-17/
laws of motion
Newton’s 3rd law of motion (NIII)
If two bodies exert forces on each
other, these forces have the same
magnitude but opposite directions.
[1][2]
“To every action, there is always opposed an equal reaction; or, the mutual
actions of two bodies upon each other are always equal, and directed to
contrary parts.” [14]: 116
Thornton, Stephen T.; Marion, Jerry B. (2004).
Classical Dynamics of Particles and Systems (5th ed.). Brooke Cole. p. 49. ISBN 0-534-40896-6.
Newton, Isaac; Chittenden, N. W.; Motte, Andrew; Hill, Theodore Preston (1846). Newton's Principia:
The Mathematical Principles of Natural Philosophy. University of California Libraries. Daniel Adee.
https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#cite_note-:0-17
forces
inertia
what can happen to the object’s motion?
‘the tendency of masses to resist changes in motion’
1.
steady force in the direction of motion: speeds up
(accelerates – increases speed at a constant rate)
It is difficult to
•
start a mass moving
•
change its direction of motion
•
stop a mass moving
in other words, it is difficult to accelerate any mass.
2.
steady force against the direction of motion: slows
down (accelerates – decreases speed at a constant
rate)
3.
steady force at right angles to direction of motion:
moves in a circle (changes direction at a constant
rate)
forces
how forces act
•
only animate objects can exert a force
•
forces only affect objects through contact
•
there is ‘more gravity the higher up you go’ … but beyond the atmosphere
there is no gravity
forces and motion
•
if an object is moving, there must be a force acting on it
•
no motion means no forces acting
•
an object stops moving when its force ‘runs out’ (force is a property of
objects)
forces in equilibrium
static equilibrium
dynamic equilibrium
all the external forces acting on an
all the external forces acting on an object
object at rest, when added up, is zero –
which is moving, when added up, is zero
that is, the external forces are in balance
– that is, the external forces are in
balance
‘sigma’
the sum of
෍ 𝑭𝑬𝒙𝒕𝒆𝒓𝒏𝒂𝒍 = 𝟎
𝐹റ𝑁𝑒𝑡
෍ 𝑭𝑬𝒙𝒕𝒆𝒓𝒏𝒂𝒍 = 𝟎
forces
interactions
forces
forces
the force of gravity causes an acceleration
•
the acceleration an object experiences close to the surface of earth is the same
for all objects
•
it is given its own letter, namely, “g”
•
g varies from place to place on the earth’s surface as the earth is not a perfect
sphere and its density distribution is not uniform
•
the general value for the magnitude of g that we will use is
F = ma → F = mg
9.81 m/s2
working with forces
Normal lines and Normal forces
•
a Normal line is an imaginary, or real, line which is
perpendicular to a surface
•
a Normal force is a force which is
perpendicular to a surface
90o
working with forces
𝐹റ𝑛𝑜𝑟𝑚𝑎𝑙
𝐹റ𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛
𝐹റ𝑔𝑟𝑎𝑣𝑖𝑡𝑦
to draw a free body diagram (FBD) isolate
the object of interest and draw all the
external forces on the object
working with forces
Surface reaction is a distributed force, but it may
A ring. The resultant acts at its centre
be replaced for convenience by its resultant, Rn.
of mass C, which is in empty space!
application of laws to free fall
application of laws to free fall
application of laws to free fall
application of laws to free fall