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# Circular motion

UCM

## Honors: Banking a car

### 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 things 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.

## Videos

Examples of centripetal force video clips

## A car going around a curve

Hewitt

### 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

## Quotes

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.
http://www.corestandards.org/Math/