___________ Circular Motion (UCM) occurs when an object moves in a circle at __________________

1. Uniform ___________ Circular Motion (UCM) occurs when an object moves in a circle at __________________ constant speed rotation ____________ axis _____________ axis revolution A. The 2 types of "Turning Around:" rotation ____________: circular motion around an axis that is ______________________ within an object revolution ____________: circular motion around an axis that is ______________________ outside of an object

2. B. Two types of Rotational/Revolutionary Speeds: 1. ____________ speed w ("omega")  _________ for all points on a solid object  units: _____________ , rpm’s, etc angular same radians/s • ___________ speed v •  depends on ______________________ of rotation or revolution •  units: _______, mph, etc •  v = ______ =_________ •  In Regents physics, ______________ is the • only type of speed we deal with linear distance from axis m/s d/t 2pr/t linear v

3. Ex: Earth Everywhere on Earth, the __________speed is the same: angular r 3600/24h w = _____________ NYS latitude 2p radians w = _____________ 24 x 3600 sec r But _________ speed v = __________ is greatest at the ______________ and zero at the _________ . equator linear 2pr/t equator rotation axis poles Rockets are launched from ____________ because its _________________________________ Florida linear speed is greatest

4. tangent • Linear velocity is always ___________ to the • circle in the _____________ of motion. direction clockwise Ex: _____________ (CW) uniform circular motion: v v 1 2 v 8 v 7 3 v 6 v 4 5 v v

5. counterclockwise Ex: __________________ (CCW) uniform circular motion: NOTICE: • In _________ CW • and CCW motion: • The __________ • (_____________ of v) • remains constant. • The ___________ • of v is changing. • Because of this, • the object must be • __________________ both v speed v magnitude 1 v 2 8 v 3 direction 7 v 6 v 4 5 v v accelerating

6. acceleration D. The direction of _________________ during UCM Δv/t • From a = _______ • a has the same • direction as ____ . vi 1 Δv Δv vf 2 where Δv = = vf – vi vf + (-vi) Δv vf -vi center • a is directed towards the circle’s _____________. • It is called ___________________ acceleration: ac. • It occurs b/c the velocity _______________________. centripetal changes direction

7. ac Ex: Direction of ____ for ____ and ______motion CW CCW 1 1 v v v v ac ac ac ac 3 3 7 7 ac ac v ac ac v v v 5 5 • Notice: • Even though a is always ____________________, • it is always _____________________ in both cases. • The angle between v and ac is always _______ . changing direction towards the center 900

8. magnitude E. The _______________ of ac is given by: ac = v2/r units of ac = [ ]2 / [ ] = = = v r (m/s)2 / m m2/s2 / m m/s2 ac ac ac ~v2 independent ~ 1 r r m v

9. F. What causes a? What causes ac? force F centripetal force Fc. Fc = = The magnitude of Fc is given by: mac m·v2/r [ ] [ ]2 / [ ] units of Fc = = = = m v r (kg) (m/s)2 / m kg m2/s2 /m kg m/s2 = N Fc Fc Fc ~v2 ~m ~ 1 r r m v

10. Fc G. Direction of ____ for ____ and ______ motion CW CCW 1 1 v v v v Fc Fc Fc Fc 3 3 7 7 Fc Fc v Fc Fc v v v 5 5 changing direction 1. Although Fc is always ___________________ , it is always towards the __________. This was also true for ac, because force F and the a that it __________ are always ____________________________ . center causes in the same direction

11. unbalanced • During UCM, the Fc is an _____________ force and Fnet ___ 0. Remember: _____________ is changing direction (even though __________ is constant), and this is an __________________ . • 3. Without Fc, the object would move off on a • ____________ (in the direction of its ___.) • 4. Fc can be provided by many different forces: • ____________ holds planets in elliptical orbits. • ____________ keeps cars on road during turns • __________________ allows birds to turn in air • _________ keeps rock turning in a circle • ________________ keeps rider on loop-d-loop ride velocity ≠ speed acceleration tangent v gravity friction air resistance string normal force

12. Ex: A 1500-kg car moves clockwise in a circle of radius 25 m at a speed of 12 m/s. Calculate a/ the centripetal acceleration of the car; b/ the centripetal force acting on the car. v2/r ac = = = (12 m/s)2/25 m v ac 5.8 m/s2 mac Fc = = = Fc (1500 kg)(5.8 m/s2) 8700 N c/ What direction are v, ac and Fc when the car is at the point shown? d/ What provides the Fc that allows the car to turn? e/ In which direction would the car move if Fc became 0? friction

13. Open your Review Book Packet to pages 44-45. Do problems #93-101