Friction & Circular Motion
Static and Moving Friction
Centripetal and Centrifugal Forces
o Friction was introduced in last lecture, expand
 Nature of Friction, its origins
 Static Friction
 Friction in Motion
o Circular motion using centripetal force
 ‘Equivalence’ with gravity
 Linear analogues
Lecture 4
o Aim of the lecture
 Concepts in Friction
 Depends on surfaces
 Depends on contact Forces
 Depends on motion
 Air resistance
 Circular Motion
 Centrifugal and Centripetal Forces

o Main learning outcomes
 familiarity with
 forces needed to sustain motion
 static and moving friction, coefficients
 Forces needed for circular motion
 Centrifugal and Centripetal force
Newton’s First Law
o Reminder: It appears that:
 A force is needed to keep an object moving at constant speed.
 An object is in its “natural state” when at rest.
o These are wrong
 friction creates this illusion.
o” Where does friction come from?
o The illustration shows two surfaces in
contact – at the microscopic level
Surfaces are NOT ‘flat’.
 ‘locked’ together
 to make them slide will require force
 to ‘break the locking’
 even when already moving
 to keep ‘breaking the locking’
Friction
o How hard it is to break the ‘locking’
will depend on:
 nature of the surfaces
 smoother, less locking
 rougher, more locking
 (also other effects ‘sticky’
surfaces like rubber)
 How hard the surfaces
are pressed together
 because the ‘true’ contact area
depends on force:
o For objects sliding over each other
o Can be described by simple equation:
F=mR
Where:
 F is the force need to overcome friction
 R is the force between the surfaces
 m is a constant which depends on the surfaces in contact
Note:
This does NOT depend on the
area in contact!
If the force BETWEEN the
surfaces, R, is the same, then
the area does not matter.
F=mR
Why is the area not important?
 Friction force depends on
Total force needed = const × (F/A) × A
o Force per unit area
o Total area
 Double area, with same TOTAL force, means
o force per unit area is halved
 So (total area) × (force per unit area) is not changed
F=mR
 m is called the coefficient of friction
o depends on BOTH surfaces
o low for ice on metal
o High for rubber on concrete
o NOTE:
o rolling friction is a different thing
 high m for rubber tyre on concrete
 Stops tyre sliding
 Helps with braking
 Does NOT resist the wheel rotating
 because there is no sliding of wheel past concrete
for rotation
F=mR
It is easier to keep something sliding than to start it moving
oThere are two coefficients of friction
 One for static friction, ms
 force needed to start a static object moving
 One for dynamic friction mr
 force needed to keep moving at constant speed
ms > mr
Easier to keep sliding than
to get moving
Approximate coefficients of friction
Static friction,
Materials
Dry & clean
Aluminum
Steel
0.61
Copper
Steel
0.53
Brass
Steel
0.51
Cast iron
Copper
1.05
Cast iron
Zinc
0.85
Concrete (wet)
Rubber
careful driving in wet! 0.3
Concrete (dry)
Rubber
1.0
Copper
Glass
0.68
Glass
Glass
0.94
Steel
Teflon
Non-stick! 0.040.04
[ 1.0 is the biggest normal value. If >1.0, then ‘sticky’.
F=mR
Often it is gravity that is creating the force
o The force due to gravity is the weight of the top object
o This is a ‘Reaction force’, hence use of ‘R’ in formula
R = Force = mg
Brass-Steel ms = 0.51
W = 10kg x 9.81 ms-1 = 98N
So F = ms x R = 98N x 0.51 = 50N
STEEL
10kg
This is the force it takes to get a
10kg steel block sliding over
a brass surface.
BRASS
The reaction force between
the surfaces is given by
R = mg cos(q)
q
The force down the slope is
F = mg sin(q)
If F > msR block will slide
mgsin(q) > msmgcos(q)
ie if tan(q) > ms
o Note that there are other forms of friction
Rolling
Pulley
Air resistance
o These do not all behave the ‘same way’ as simple sliding
 eg for many situations the force due to air resistance is
F = k v2
o Where v is the velocity and k a constant which depends on
 Air density
 Shape of object moving through air.
kplane < kbus
Supersonic plane
(at same altitude of flight)
Circular Motion
It takes a force to
change the direction
of a moving object
motion
force
oIf a constant force is always applied
perpendicular to the motion
then
the object will go in a Circle
Its speed will not change
Just the direction alters
•The force of gravity does this, keeping planets in orbits
The force of the sun is always towards the sun
Which is perpendicular to the direction the plants travel
(not quite a circle – but don’t consider that here)
The force needed to make a circle is:
r
F
Where
m is the mass of the circling body
v is its speed
r is the radius of the circle
the force is called the centripetal force
v
If the body is made to circle by
a string, then the string will feel
a force pulling it into tension.
This is the centrifugal force.
Of course these two different names
are really describing the same force.
But from different perspectives
o Centripetal
Force applied to make circular motion
o Centrifugal
Force ‘felt’ by object being made to circle
Riders feel the
centrifugal force
holding them in
the car.
The rail applies
a centripetal force
to make the car
circle.
Riders ALSO
feel gravity,
but it is not enough
to make them fall
out of the car
It is common to use w instead of v, where
w = v/2pr
This is the angular speed
- number of radians per second
Then the centripetal force is:
F = w2r
With F = mR (concrete-rubber m = 1.0) and F = mv2/r
can answer question:
How fast can you drive your Ferarri round a corner?
Answer:
Depends
on the
speed limit
I cant afford
a Ferarri,
Ferarri
but in theory:
Consider a real car (Lotus Elise)
v
r
Centripetal force
o Force needed to make the car turn in circle

Fcircle = mv2/r
o Force provided by friction between wheel and road
 Ffriction = mR where R = mg
o If Fcircle is greater than Ffriction then friction will not be enough
 and Elise will slip
(but designed with oversteer so will slip rear end first – chance to recover)
Condition is mv2/r = mmg
=>
v = √(mgr)
Answer: v = √(mgr)
(BUT remember m is much
smaller in the wet!)
Finally, when cornering:
remember that F = mR
o R can be bigger if the car has proper aerodynamics
 The reason cars have ‘wings’ on them is to
force the car down increasing R to a bigger value
than mg, [it flies into the ground]
o In formulae 1, the cars are designed so R is very large,
 the cars stick like limpets round the corners,
 but only if they go fast, so R is larger than mg!