Circular Motion A straight line may be the

Circular Motion A straight line may be the shortest distance between two points, but it is by no means the most interesting.

Circular Motion • While most of the motion we’ve covered thus far has to do with straight vectors, much of motion also happens in circular paths. • Review: – The circumference of a circle: • d=2πr

Speed • Average Speed= Change in Distance/Change in Time (Δd/Δt) • Circular distance = Circumference = 2πr • So the speed of an object in constant circular motion = 2πr/t – Or the circumference of the circle divded by the time it takes to make one trip around that circle.

Velocity • Remember: Speed and Velocity are different (scalar vs. vector). • Velocity is still a vector, even in circular motion.

Velocity and Acceleration • Although the speed around a circle remains the same, its velocity is constantly changing because velocity is both a magnitude and a direction. • Thus, if velocity is in constant state of change, it is experiencing acceleration.

Acceleration and Force • Following that same line of thinking, if acceleration is being experienced by a mass, then the mass must be being acted upon by a FORCE. • The acceleration a mass experiences in circular motion is called centripetal acceleration.

Acceleration and Force • Centripetal Acceleration: ac = v 2/r *For circular motion equations, v is used for speed, rather than an instantaneous velocity vector.

Acceleration and Force • Important formulas to recall: – The circumference of a circle: d = 2πr – Velocity = d/t • Formula Derivation: – ac = v 2/r = ((2πr)/t) 2/r = 4π2 r/t 2

Acceleration and Force • A rock tied to a string is traveling at a constant speed of 4 m / s in a circle of radius 1. 5 m. Calculate the magnitude of the centripetal acceleration of the rock. What is the direction of the acceleration?

Acceleration and Force • A rock tied to the end of a string moves in a circle at a constant speed of 2. 5 m / s and experiences an acceleration of 4. 0 m / s 2. What is the radius of the circle of its motion?

Centripetal Force • ‘Centripetal’ means ‘center seeking’. • Thus, Centripetal Force is the force that is directed at the center of a rotation; the force that is pushing a circular moving (or accelerating) body inward toward the center, keeping it moving in a circular path, rather than its natural state of a straight vector.

“Centrifugal” Force • “Centrifugal” Force is NOT the same as Centripetal Force – in fact, it isn’t even a real force at all. • The misconception is that centrifugal force is an outward force, but it really isn’t a force at all. • The ‘outward force’ experienced by a mass in circular motion is simply its natural inertia at work in an accelerating body.

“Centrifugal” Force • “Centrifugal” Force is NOT the same as Centripetal Force – in fact, it isn’t even a real force at all. • The misconception is that centrifugal force is an outward force, but it really isn’t a force at all. • The ‘outward force’ experienced by a mass in circular motion is simply its natural inertia at work in an accelerating body.

“Centrifugal” Force • “Centrifugal” Force is NOT the same as Centripetal Force – in fact, it isn’t even a real force at all. • The misconception is that centrifugal force is an outward force, but it really isn’t a force at all. • The ‘outward force’ experienced by a mass in circular motion is simply its natural inertia at work in an accelerating body.

Centripetal Force • Centripetal Force: Fc = mv 2/r *For circular motion equations, v is intended as speed, rather than an instantaneous vector.

Centripetal Force • A 250 kg motorcycle is driven around a 12 meter tall vertical circular track at a constant speed of 11 m/s. What is the centripetal force acting upon the motorcycle as it goes around the track?

Centripetal Force • A 500 kg race car rounds a curve with a radius of 100 m. – What type of force is the centripetal force in this example? – Find the magnitude of the centripetal force acting on the car when it rounds the curve at 20 m/s. – Find the magnitude of the centripetal force acting on the car when it rounds the curve at 60 m/s. – How does the centripetal force at 60 m/s compare to the centripetal force at 20 m/s?

Centripetal Force • A 1. 3 m long fishing line rated as "10 lb test" that can withstand a force of up to 10 lb (44. 48 N) is attached to a rock of mass 0. 5 kg. Calculate the maximum speed at which the rock can be rotated without breaking the line.

Centripetal Force • A car of mass 1000 kg travels around a level curve of radius 40 m. If the maximum frictional force that can be exerted upon the car by the road (determined by the coefficient of friction between the tires and the road) is 7000 N, how fast can the car travel without "spinning out? "

Individual Practice • Page 162 – 12 -15 • Page 163 – 21 -24 • Do them alone first, then compare with your classmates afterwards.