SPINSPINSPINSPINSlides created by Slides created by Kathy BucklandKathy Buckland

at the University of Britishat the University of British

What’s Happening Here?

• An example of circular motion

What is Circular Motion?

• The circular path along which an object travels

• The rotation around a fixed axis

What is the word used to describe this path?

ORBIT

Examples • Rollercoaster• Swinging an object on a string• Planetary objects-moon, satellites, etc.• Car going around a round-about

Back to the mid 1600’s…

Newton’s Second Law:

“Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis

illa imprimitur”-Principia Mathematica

(1687)

Otherwise known as…

maF F=force (N)m=mass (kg)a=acceleration (m/s2)

F=maWhat is FORCE?

• PUSH

or a…

• PULL

Examples of Forces

• Gravity

• Impact Forces

• Tension

• Friction

Circular Motion and Force

How does the object stay in its path?

This force is called…

CENTRIPETAL FORCEcentrum "center" and petere “go to” or

“seek”To get where you want “to go”, you must….

PEDAL….

Not a new force !!

Examples of forces:• Gravity• Impact Forces

Examples of these “acting” as theCENTRIPETAL FORCE

• Ball on a string• Rollercoaster

• Tension• Friction

• Planetary Motion• Car going in

circles

MASS• The amount of MATTER an object contains• Not weight -weight changes depending

on gravitation field

maF What next?

and finally…

ACCELERATION

How the velocity changes in a certain amount of time

In physics lingo

maF

t

va

a=acceleration (m/s2)Δ= “change in”v=velocity (m/s)t=time (s)

2007 Lamborghini Murcielago LP640

acceleration: 0-62 mph time of 3.4 seconds(0-100km/h in 3.4 seconds!)

ACCELERATION

How the velocity changes in a certain amount of time

In physics lingo

• a=acceleration (m/s2)• Δ= “change in”• v=velocity (m/s)• t=time (s)

maF

t

va

Velocity vs. Speed

• Velocity has a DIRECTION and a MAGNITUDE

• The speed is the MAGNITUDE

How do we represent direction and magnitude?

VECTORS

Vector Recall

The length of the vector represents the

MAGNITUDE or SPEED The direction it points is the

DIRECTION

Adding: Subtracting:a

b

a-b

a

b

a+b

Back to Circular Motion…

How can we find the force it takes to hold on object in orbit?

Remember:

Δv is a change in direction not magnitude

maF

t

va

DEMO # 1DEMO # 1DEMO # 1DEMO # 1Finding centripetal accelerationFinding centripetal acceleration

What will it be?

How do we get centripetal acceleration ?

A little geometry and algebra…

Three more steps..1. Make a tiny triangle so..• have a right triangle• use sinθ = opposite hypotenuse

• sin θ = θ 2. Use similar triangles3. Use some algebra

t1

t2

S=v(t2-t1)=vΔt

Find similar triangles

Centripetal acceleration is…

r

vacent

2

Finally put it all together…

For circular motion…

t

vmmaF

r

vmmaF centcent

2

Now What’s Happening Here?

• Our starting example of circular motion

What to remember

• What circular motion is- be able to recognize it• Newton’s Second Law- you will see it again!

• That velocity has direction and speed• Centripetal acceleration deals with the change

in direction• Things that effect centripetal force are mass,

velocity, and the distance from the center

maF

r

vmFcent

2