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# Circular motion

### Uniform Circular Motion (UCM) is motion in a circle of constant radius at constant speed. http://www.physicsclassroom.com/mmedia/circmot/ucm.cfm

### But the direction is always changing. UCM

### The direction of the acceleration always points inward. ### Acceleration is always perpendicular to the velocity. ## Period and Frequency

### Look at this animation: How long does it take to make one revolution? That amount of time is T, the period. ## Centripetal velocity and acceleration

### Therefore V =  circumference / time  = ### Every physics textbook has a proof. Here we just state the result: ### We also may write the acceleration in terms of T (period) ## So     F  = m·v2/r

### It calculates centripetal force, using radius (r), period (T) and mass (m) (right click on it to expand.) ## Direction of centripetal force

### Think about a ball on a string. We see that the direction of the centripetal force must be inward. (If there was no inward force then the ball would fly outwards!) ### It’d fly off in a straight line (Newton’s 1st law of motion!) ### When a car goes around a curve, there must be a net force towards the center of the circle of which the curve is an arc. If the road is flat then that force is supplied by friction. ### If the frictional force is insufficient then the car will tend to move more nearly in a straight line, as the skid marks show. ## Honors: Banking a car

### In fact, for every banked curve, there is one speed where the entire centripetal force is supplied by the horizontal component of the normal force, and no friction is required. ### This occurs when ### What’s happening here? Explain using the concepts covered in this unit. ### 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

### So why are you forced left/outward? In actuality, the car is turning, while you continue in a straight path! http://www.physicsclassroom.com/mmedia/circmot/rht.cfm

### 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/