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Circular motion

people-travel-to-wonder-circular-motion-saint-augustine

For our unit on the Coriolis effect see Coriolis effect on Kaiserscience.

Uniform circular motion:
motion of an object in a circle, at a constant speed

Keep track of position and speed!

     r = radius = position vector

     v = velocity vector

circle

UCM

The direction of the velocity is always TANGENT to the circle!

uniform-circular-motion

circular acceleration always points inward.

called centripetal acceleration.

So direction of acceleration is always
perpendicular to the velocity.

http://www.slideshare.net/rtrujill/lecture-ch-05

period       =  T
time for one revolution around the circle

frequency =  f
# of revolutions per second.

             f = 1 / T

             T = 1 /  f

Look at this image – how long does it take to make one revolution? That’s the period.

uniform-circular-motion

Centripetal acceleration

centripetal-acceleration

v  =  speed of object

R = radius of circle

v  =  distance / time  =  circumference / time  =

circular-speed

Write acceleration in terms of T (period)

centripetal-acceleration-another

Newton’s Second Law

F = ma        and       a = v2/r

So     F  = m·v2/r

Here’s a computer program written in Scratch that calculates centripetal force, using radius (r), period (T) and mass (m.)

scratch-example

http://www.slideshare.net/rtrujill/lecture-ch-05

http://www.slideshare.net/rtrujill/lecture-ch-05

http://www.slideshare.net/rtrujill/lecture-ch-05

What’s happening here?

man-in-hole-centripetal-force-normal-force

PhysicsFootnotes writes:

As he rises, the radius of the hole increases, and the faster he has to run to generate a normal reaction force which (combined with friction) has a sufficient vertical component to balance his weight.

Just like the thingee you put the coins in, only in reverse.

How fast would he need to run, in order to do this?

Set up a force-vector diagram. His centripetal acceleration has a value of v-squared/r.

Increasing r means you have to increase v to compensate.

https://www.facebook.com/physicsfootnotes

Videos

https://www.youtube.com/watch?v=QH2TgwGlFQ0

additional centripetal force figures
Centripetal force circular

What forces exist when a car is going around a curve?

What force does the car put on the road?
What force does the road put on the car?

Hewitt

Hewitt

You’re a passenger in a car, making a right-hand turn.
As the car turns right, you begin sliding to the left.
The car is turning to the right, due to the inward force
(tires against road, and road back against the tires)

So why are you forced left/outward?
In actuality, the car is turning, while you continue in a straight path!

G forces on a roller coaster

g-forces-on-a-roller-coaster

Full discussion here: http://www.physicsclassroom.com/mmedia/circmot/rcd.cfm

Resources

PowerPoint Chap 10 Circular Motion Hewitt

Physics PowerPoints holtonsworld.com

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion is a mathematical model describing change in motion (the acceleration) of objects when acted on by a net force.

HS-PS2-10 (MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations

 

Massachusetts Science and Technology/Engineering Curriculum Framework (2006)

1.8 Describe conceptually the forces involved in circular motion.

SAT Physics Subject Test Learning Objectives

Circular motion, such as uniform circular motion and centripetal force

Common Core Math

CCSS.MATH.CONTENT.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
CCSS.MATH.CONTENT.8.EE.C.7 Solve linear equations in one variable
CCSS.MATH.CONTENT.HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (including isolating a variable)
CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
http://www.corestandards.org/Math/

 

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