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

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

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

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

Ex: __________________ (CCW) uniform circular motion: counterclockwise 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 v speed magnitude 1 v 2 8 v 3 7 direction v 6 v 4 5 v v accelerating

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

Ex: Direction of ____ for ____ and ______motion CW CCW ac Ex: Direction of ____ for ____ and ______motion CW CCW 1 v v 1 v ac ac v ac ac 3 7 3 7 ac ac v ac ac v v 5 5 v 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

E. The _______________ of ac is given by: 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 ~ 1 r independent v r m

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

G. Direction of ____ for ____ and ______ motion CW CCW Fc G. Direction of ____ for ____ and ______ motion CW CCW 1 v v 1 v Fc Fc v Fc Fc 3 7 3 Fc Fc 7 v Fc Fc v v v 5 5 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 ____________________________ . changing direction center causes in the same direction

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 unbalanced ≠ velocity speed acceleration tangent v gravity friction air resistance string normal force

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. ac = = v2/r (12 m/s)2/25 m v ac 5.8 m/s2 Fc = = mac 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