Chapter 9 Circular Motion

The time it takes for 1 full rotation of an object. How long??? Period The time it takes for 1 full rotation of an object. T = 1/ƒ Period = 1/frequency s = 1/Hz

The number of rotations per unit of time. How many?? Frequency The number of rotations per unit of time. Measured in Hz. (Hertz)

Linear (Tangential) Speed When an object spins in a circle… distance = circumference vc = 2πr T Linear speed = 2π * radius Period m/s = m s

Please note… An object can move around a circle with a CONSTANT SPEED, yet still be accelerating! How????????? Because its direction is always changing!

Centripetal Acceleration Always directed toward the center of the circle. ac = v2 r Centripetal acc = (linear speed)2 radius m/s2 = m/s m

Centripetal Force Fc = mac Always directed toward the center of the circle. Fc = mac Centripetal force = mass * centripetal acc. N = kg * m/s2

Example 1 After closing a deal with a client, Kent leans back in his swivel chair and spins around with a frequency of 0.5 Hz. What is Kent’s period of spin? T = 1/ƒ 2 s

Example 2 Curtis’ favorite disco record has a scratch 0.12 m from the center that makes the record skip 45 times each minute. What is the linear speed of the scratch as it turns? 1st find the period: T = 1/f T = 1.3 s 2nd find the linear speed: v = 2πr/T V = .58 m/s

Example 3 Missy’s favorite ride at the fair is the rotor, which has a radius of 4.0 m. The ride takes 2.0 s to make one full revolution. What is Missy’s linear speed? v = 2πr/T v = 13 m/s What is Missy’s centripetal acceleration? ac = v2/r ac = 42 m/s2

Example 4 Captain Chip pilots a 60,500 kg plane. He must circle above the airport to wait his turn to land. If Chip flies his plane in a circle whose radius is 50,000. m every 1,800. s, what centripetal force must the air exert against the wings to keep the plane moving in a circle? First, find the speed: v = 2πr/T v = 175.0 m/s Next find centripetal force: Fc = mv2/r Fc = 37,100 N

Abby 

Which trajectory does the ball follow? A ball on a string is swung in a circle. The string breaks. Which trajectory does the ball follow? A? B? C? D? STT7.5 C. The line that is tangent!!

path of ball if the string Ball on a string The tension in the string provides the necessary centripetal force to keep the ball going in a circle. path of ball if the string breaks

The net force is towards the center! Centripetal Force The force required to cause an object to follow a circular path. Centripetal means “center seeking” The net force is towards the center!

A car turning a corner… MUST have a centripetal force in order to put it into a circular path! Friction between the road and tires is the centripetal force. No friction (ice) = No centripetal force  This makes the car slide.

Centrifugal force Centrifugal means “center fleeing.” The red object will make the turn only if there is enough friction on it…otherwise it goes straight. The apparent outward force is called the centrifugal force… But it isn’t a force at all-it’s actually the absence of a centripetal force!!! object on the dashboard straight line object naturally follows

Silly Silo (Rotor) Friction between Bart and wall Bart’s weight wall pushing in on Bart Bart’s weight The inward wall force keeps Bart in the circle. Friction keeps him from falling down.

Very little gravity in space…

Very little gravity in space…

But we can make our own to make it easier! Space Station But we can make our own to make it easier! The faster it rotates, the more people will weigh. The International Space Station

Ladybug on the inside of a bike tire… Just like the space station, it would feel like gravity for the ladybug!!! The faster the bike goes, the more the ladybug will weigh!

Ladybug on a Turntable Why??? Which ladybug has a greater velocity? The inside ladybug. The outside ladybug. The outside ladybug! Why??? It must cover more distance in the same amount of time!

Basically, the velocity depends on the radius. Larger radius = larger velocity! Smaller radius = smaller velocity!

Goal: The weight (N) hanging down = the Centripetal Force (N) Lab Set Up tape Goal: The weight (N) hanging down = the Centripetal Force (N)