1. Friction & Circular Motion
Static and Moving Friction
Centripetal and Centrifugal Forces
Friction was introduced in last lecture, expand
Nature of Friction, its origins
Static Friction
Friction in Motion
Circular motion using centripetal force
‘Equivalence’ with gravity
Linear analogues

2. Lecture 4 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
  Main learning outcomes
familiarity with
forces needed to sustain motion
static and moving friction, coefficients
Forces needed for circular motion
Centrifugal and Centripetal force
Lecture 4

3. Newton’s First Law 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.
These are wrong
friction creates this illusion.
” Where does friction come from?
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’

4. Friction 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:

5. F = m R Where: F is the force need to overcome friction
For objects sliding over each other
Can be described by simple equation:
F = m R
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.

6. F = m R Why is the area not important? Friction force depends on
Force per unit area
Total area
Double area, with same TOTAL force, means
force per unit area is halved
So (total area) × (force per unit area) is not changed
Total force needed = const × (F/A) × A

7. F = m R m is called the coefficient of friction
depends on BOTH surfaces
low for ice on metal
High for rubber on concrete
NOTE:
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

8. F = m R
It is easier to keep something sliding than to start it moving
There 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

9. [ 1.0 is the biggest normal value. If >1.0, then ‘sticky’.
Approximate coefficients of friction
Materials
Dry & clean
Aluminum
Steel
0.61
Copper
0.53
Brass
0.51
Cast iron
1.05
Zinc
0.85
Concrete (wet)
Rubber
careful driving in wet! 0.3
Concrete (dry)
1.0
Glass
0.68
0.94
Teflon
Non-stick!
Static friction,
[ 1.0 is the biggest normal value. If >1.0, then ‘sticky’.

10. F = m R Often it is gravity that is creating the force
The force due to gravity is the weight of the top object
This is a ‘Reaction force’, hence use of ‘R’ in formula
R = Force = mg

11. Brass-Steel ms = 0.51
W = 10kg x 9.81 ms-1 = 98N
So F = ms x R = 98N x 0.51 = 50N
This is the force it takes to get a
10kg steel block sliding over
a brass surface.
STEEL
10kg
BRASS

12. The reaction force between
the surfaces is given by
R = mg cos(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 q

13. (at same altitude of flight)
Note that there are other forms of friction
Rolling
Pulley
Air resistance
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
Where v is the velocity and k a constant which depends on
Air density
Shape of object moving through air.
kplane < kbus
(at same altitude of flight)
Supersonic plane

14. It takes a force to change the direction of a moving object motion
Circular Motion
It takes a force to
change the direction
of a moving object
motion
force
New motion

15. If 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

16. 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)

17. r F v The force needed to make a circle is: 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 r F v

18. 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
Centripetal
Force applied to make circular motion
Centrifugal
Force ‘felt’ by object being made to circle

20. 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

21. 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

22. Answer: Depends on the speed limit
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
Answer: I cant afford a Ferarri, but in theory:
Answer: I cant afford a Ferarri

23. Consider a real car (Lotus Elise)v r
Centripetal force
Force needed to make the car turn in circle
Fcircle = mv2/r
Force provided by friction between wheel and road
Ffriction = mR where R = mg
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)

24. Answer: v = √(mgr) (BUT remember m is much smaller in the wet!)

25. Finally, when cornering:
remember that F = mR
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]
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!