Circular Motion Kathy Buckland

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… F=force (N) m=mass (kg) a=acceleration (m/s 2 )

F=ma What 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 FORCE centrum "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 the CENTRIPETAL FORCE Ball on a string Rollercoaster Tension Friction Planetary Motion Car going in circles

What next? MASS The amount of MATTER an object contains Not weight -weight changes depending on gravitation field

and finally… ACCELERATION How the velocity changes in a certain amount of time In physics lingo  a=acceleration (m/s 2 ) 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/s 2 ) Δ= “change in” v=velocity (m/s) t=time (s)

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: (remember) 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

DEMO # 1 Finding 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 triangles 3. Use some algebra t1t1 t2t2 S=v(t 2 -t 1 )=vΔt Find similar triangles

Centripetal acceleration is…

Finally put it all together… For circular motion…

DEMO # 2 Observing the relationship

The difference in force holding the object in circular motion can be seen as the device spins. As the velocity increases the changes in force become greater.

Force comparisons… Compare to lifting up objects- Remember acceleration is gravity≈10 m/s 2 1 N≈ force required to hold up an orange 10 N≈ force required to hold this weight Force to lift an elephant? m ≈ 4500 kg so… F ≈ N !! like lifting oranges

And us ? Mass Earth ≈ 6 x kg v ≈ m/sec r ≈1.5 x m F ≈ 3.6 x N Like lifting about 8 x or 800 million billion elephants !!

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

DEMO # 3 Observing Circular Motion