A2 lesson, force in a circle Describe qualitatively motion in a curved path due to a perpendicular force, and understand the centripetal acceleration in the case of uniform motion in a circle Express angular displacement in radians Recall and use centripetal acceleration a = v2/r Apply the equation F = ma to uniform motion in a circle to derive F = mv 2/r

1. Force in a circle

2. The Bucket of water
• How does he not get wet?
• What would happen if the handle snaps?
http://www.youtube.com/watch?v=EPWmGttDCNY&feature=related

3. Lesson Objectives
• Describe qualitatively motion in a curved
path due to a perpendicular force, and
understand the centripetal acceleration in
the case of uniform motion in a circle
• Express angular displacement in radians
• Recall and use centripetal acceleration
a = v2/r
• Apply the equation F = ma to uniform
motion in a circle to derive F = mv 2/r

4. What are the forces?
centripetal” means
“centre seeking”.
Centripetal is an
adjective describing
the force; it is not the
name of a special
type of force, such as
tension, gravity,
magnetic force etc -
e.g. pulling the bucket
in with the rope
centrifugal, or centre-fleeing e.g. the force of
the bucket on my hand
Planetary orbits (almost!) gravitation
Electron orbits electrostatic force on electron
Centrifuge contact force (reaction) at the walls
Gramophone needle the walls of the groove in the record
Car cornering friction between road and tyres
Car cornering on banked
track
component of gravity
Aircraft banking
horizontal component of lift on the
wings

5. Newton's 3rd law….
Every force has an equal
and opposite reaction, so
the force produced from
the air, pushes the balloon
in the opposite direction

6. A force cannot exist on its own – there is always a second force acting against it.
This forms the basis of Newton’s third law of motion states, which states:
What is Newton’s third law?
These pairs of forces that act between two objects are sometimes called action–reaction
pairs.
If object A exerts a force on object B, then object B exerts an equal but
opposite force on object A.

7. Centrifugal and Centripetal Force
•The centripetal force is
directed inward, towards
the axis of rotation
•As you swing the ball with
the string, you feel the
string tug on you hand....,
this is called the centripetal
force and is equal and
opposite to the centrifugal
force...

8. the difference between linear and
angular velocity
• The instantaneous linear velocity at a point in
the circle is usually given the letter v and
measured in metres per second (m s-1).
•The angular velocity is the angle through which the radius to this point on the
circle turns in one second. This is usually given the letter w (Greek omega)
and is measured in radians per second (rad s-1)
http://www.animations.physics.unsw.edu.au/jw/circular.htm

9. Deriving the formula for centripetal acceleration in
terms of angular velocity
Consider an object of mass m moving with constant angular velocity (w)
and constant speed (v) in a circle of radius r with centre O.
It moves from P to Q in a time t.
The change in velocity Δv is parallel to PO and Δ v = v
sinθ
When θ becomes small (that is when Q is very close to
P) sinθ is close to θ in radians.
So Δ v = v θ
To find the change in acceleration divide both sides by t
a = Δ v / t = v θ / t
Angular speeds w = θ / t,
a = v w
Since we also have v = w r (derived from last lesson), this can be written as
a = v2/r = v w = w2r
Applying Newton's Second Law (F = ma) gives:
F = mv2/r = m vw = m w2 r
w = v / r

10. The important formulas
a= v2 / r F = Force (newtons)
V = Velocity (m/s)
r = Radius (m)
m = Mass (kg)
w = radial velocity rad s-1
F = m v w = m w2 r

11. The turn table demo
How long will these objects stay on?
What forces are acting on these
objects?
Where is the best place to put the
object to make it fly off the turntable
1. When a car turns a corner it can sometimes skid. Explain why, using the
words velocity, friction, force

12. Plenary - Answer This Question
1)You are sitting in the seat of a rollercoaster. Your mass is
50kg and the mass of the rollercoaster is 1000kg. You are
travelling at a speed of 20 m/s. The centripetal force
acting on you is 1000N. What is the radius of the ‘loop the
loop’ you are travelling around? Draw a diagram of the
rollercoaster and label the forces acting on it.