1. Circular Motion Aim: How do objects travel in circular paths?

2. Circular Speed Radius – The distance from the center of the circle to the perimeter Diameter – The distance that passes through the center of the circle with endpoints that lie on the circle; ( 2×Radius ) Circumference – The distance AROUND the circle; ( 2πr ) Period – The time it takes to complete ONE REVOLUTION Radius Circumference Diameter

3. Circular Speed Radius Circumference Diameter

4. Circular Speed vs. Tangential Velocity The circular speed of an object will always be constant (in this course) The MAGNITUDE of the velocity will be constant but its DIRECTION always changes Therefore, Tangential Velocity is NOT CONSTANT and always points STRAIGHT OUTWARD vcvc vcvc vcvc vcvc vcvc vcvc vcvc vcvc

5. Centripetal Acceleration Centripetal  “Center Seeking” An object is still ACCELERATING when it changes DIRECTION, even though the MAGNITUDE of the velocity stays the same Centripetal Acceleration Units: (m/s 2 ) Circular Speed -OR- Tangential Velocity Units: (m/s) Radius Units: (m)

6. Centripetal Acceleration vcvc vcvc vcvc vcvc vcvc vcvc vcvc vcvc acac

7. Example #1 A lady bug flies in a horizontal circle that has a radius of 0.7m and completes the cycle every 2.3 seconds. Determine the magnitude of the lady bug’s (a) speed and (b) the centripetal acceleration

8. Centripetal Force In order for an object to accelerate, an unbalanced force must be present Centripetal Force Units: Newtons (N) Circular Speed -OR- Tangential Velocity Units: (m/s) Radius Units: (m) Mass Units: Kilograms (kg) Centripetal Acceleration Units: (m/s 2 )

9. Centripetal Force vcvc vcvc vcvc vcvc vcvc vcvc vcvc vcvc FcFc

10. Centrifugal Force From an INERTIAL FRAME OF REFERENCE, the centrifugal force DOES NOT EXIST – This is the reference frame that we always view from in this class However, from the ROTATING FRAME OF REFERENCE, the centrifugal force causes objects to move radially outward ROTATING INERTIAL

11. Example #2 An F15 fighter jet (1.3×10 4 kg) makes a horizontal turn of radius 540m at a speed of 340m/s. Calculate the magnitude of the centripetal force acting on the jet

12. G-Suit The g-suit helps prevent blood from pooling to the lower extremities of the pilot when experiencing high acceleration (g-force) When this occurs the brain is deprived of blood (Hypoxia) Extended periods of Hypoxia causes the pilot to greyout, followed by tunnel-vision, then blacking out, and finally losing consciousness g-induced Loss of Consciousness (g-LOC)

13. Example #3 A man swings a 0.5kg ball above his head in a horizontal circle that is attached to a 0.8m long string. If the ball moves at a uniform speed of 10m/s, calculate the tension in the string F T = F c

14. Example #4 A 1800kg car with rubber tires drives on a dry asphalt circular track that is 100m in diameter. Calculate the maximum speed the car can travel at, without skidding out of control. FfFf FNFN FgFg

15. A performer spins fire poi (0.5kg) in a vertical circle of radius 0.7m at a uniform speed of 12m/s. Calculate the tension in the string at the (a) top and (b) bottom of the circle FTFT FgFg FTFT FgFg

16. Calculate the maximum speed at which the 5000kg roller coaster can travel at in order for the passengers to feel “weightless” when going over a hill that has a radius of 30m. FNFN FgFg

17. SUMMARY How would you calculate the speed of an object travelling in a circle? Describe the difference between circular speed and tangential velocity Define “centripetal” How would you calculate the centripetal acceleration? How would you calculate the centripetal force?