Circular Motion

Period and Frequency A CD rotates in a player at a constant speed of 240 rpm. –How frequently does it complete a revolution: In minutes? In seconds? –How long does it take to complete one revolution?

Period and Frequency Period (T): The time it takes for an object in circular motion to make one complete revolution (or cycle) –Unit: s/rev – s/cycle – seconds Frequency (f): The number of revolutions, or cycles, in a given period of time –Equation: –Unit: 1/s – s -1 – Hertz (Hz)

Speed of an Object traveling in a Circle A car traveling in a circle with a radius of 40 m. –How far does it travel per cycle? The car completes 5 revolutions per minute. –What is its period? (How long does it take to complete a rev?) What is the car’s speed? –

5 m 10 m Each Revolution takes 2 seconds What was the distance traveled by box 1? 21 What was the distance traveled by box 2? What was the speed of box 1? What was the speed of box 2?

Centripetal Acceleration Velocity is a Vector – Magnitude (i.e. size) – Direction –Speed is constant, direction changing with time –  Velocity is changing with time, thus accelerating v v After 2 Sec v After 3 Sec v After 6 Sec After 5 Sec v After 4 Sec v After 7 Sec v

Centripetal Acceleration: The acceleration of an object traveling in a circle at a constant speed –Speed is constant –Direction is changing –Acceleration vector points inward (center seeking) Centripetal Acceleration v acac

vfvf -v i Centripetal Acceleration Why does the acceleration vector point inward? vivi vfvf vivi -v i vfvf

Centripetal Force a c, centripetal acceleration (m/s 2 ) –“Center seeking” –Necessary to keep the object traveling in a circle F c, centripetal force (N) –Newton’s 2 nd Law Newton’s 2 nd Law for Circles NOTE: CENTRIFUGAL FORCE IS AN IMAGINARY FORCE TO EXPLAIN INERTIA! DOES NOT EXIST!

Centripetal Force The centripetal acceleration is caused by another force such as: –Friction –Tension –Normal Force –Gravity

Centripetal Force Steps to solve centripetal force problems: –Draw a free body diagram –Identify the force causing the centripetal force The force that is keeping the object going in a circle –Set the causal force = centripetal force eq. –Solve for unknown

A 0.50 kg box is attached to string on a frictionless horizontal table. The box revolves in a circle of radius 2.8 m. If the box completes 1 revolution every 2.0 seconds, what is the tension in the string? r The centripetal force is caused by…the tension in the string FNFN FgFg FTFT We know m & r, but need v

A 1200 kg car approaches a circular curve with a radius of 45.0 m. If the coefficient of friction between the tires and road is 1.20, what is the maximum speed at which the car can negotiate the curve? r FNFN FgFg FfFf (Car is going into the page and turning right) The centripetal force is caused by…friction