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Circular motion

Content objective:

What are we learning? Why are we learning this?

content, procedures, skills

Vocabulary objective

Tier II: High frequency words used across content areas. Key to understanding directions, understanding relationships, and for making inferences.

Tier III: Low frequency, domain specific terms

Building on what we already know

What vocabulary & concepts were learned in earlier grades?
Make connections to prior lessons from this year.
This is where we start building from.

For our unit on the Coriolis effect see Coriolis effect.

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



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


circular acceleration always points inward.

called centripetal acceleration.

So direction of acceleration is always
perpendicular to the velocity.


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.


Centripetal acceleration


v  =  speed of object

R = radius of circle

v  =  distance / time  =  circumference / time  =


Write acceleration in terms of T (period)


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.)





What’s happening here?


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.




additional centripetal force figures

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?



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


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


Physics of Batman The Dark Knight


PowerPoint Chap 10 Circular Motion Hewitt

Physics PowerPoints holtonsworld.com


As the small pebble stirs the peaceful lake; The centre mov’d, a circle straight succeeds, Another still, and still another spreads.
– Alexander Pope, Essay on Man (ep. IV, l.364)

People travel to wonder at the height of mountains, at the huge waves of the sea, at the long courses of rivers, at the vast compass of the ocean, at the circular motion of the stars; and they pass by themselves without wondering.
– Saint Augustine of Hippo (354 – 430 CE)


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.

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