Chapter 9 Circular Motion Conceptual Physics Chapter 9

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Chapter 9 Circular Motion Conceptual Physics Chapter 9 1

Chapter 9 Circular Motion Conceptual Physics Chapter 9 1

Rotation and Revolution ¤ Any object that is turning does so about an imaginary

Rotation and Revolution ¤ Any object that is turning does so about an imaginary straight line called the axis. ¤ If the axis is located within the turning body (internal), the motion is called a rotation. ¤ If the axis is located outside of the turning body (external), the motion is called a revolution. Conceptual Physics Chapter 10 2

Rotation and Revolution REVOLUTION ROTATION While. The the disc bug ROTATES REVOLVES about an

Rotation and Revolution REVOLUTION ROTATION While. The the disc bug ROTATES REVOLVES about an external its internal axis Conceptual Physics Chapter 10 3

Tangential Speed ¤ Linear speed is the distance traveled per unit time. s =

Tangential Speed ¤ Linear speed is the distance traveled per unit time. s = r d t 2πr = T The If antime tangential object it takes travels speed tocan once ofbe circumference complete the around body a circular is precisely thewhere linear path, one found by 2πr, r isit circular speed travels along apath distance is called circular equal the radius ofthe circle. the path. to the period circumference and is of represented the circle. by T. Conceptual Physics Chapter 10 4

Tangential Speed The linear speed of the ball at any given instant is always

Tangential Speed The linear speed of the ball at any given instant is always directed tangent to the circular path. Conceptual Physics Chapter 10 5

Rotational Speed ¤ The rotational speed or angular speed is the number of rotations

Rotational Speed ¤ The rotational speed or angular speed is the number of rotations per unit time. ¤ Rotational speed is commonly measured in RPM (rotations/revolutions per minute). ¤ We use the Greek letter omega (ω) to represent rotational speed. ¤ Example: ω = 30 RPM Conceptual Physics Chapter 10 6

Rotational Speed The tangential Two objects placed speedonand the samerotational the rotating platform speed

Rotational Speed The tangential Two objects placed speedonand the samerotational the rotating platform speed arewill have theby related same rotational speed. v = r·ω The object furthest …and the greater the The faster the platform from the center of radial distance, the spins, the greater the rotation will have the tangential speed will speed. be at greater tangential greatestthe tangential any point the platform. speed willon be. Conceptual Physics Chapter 10 7

Question On a merry-go-round, the horses along the outer rail are located three times

Question On a merry-go-round, the horses along the outer rail are located three times farther from the axis of rotation than the horses along the inner rail. If a boy sitting on one of the inner horses has a rotational speed of 4 RPM and a tangential speed of 2 m/s, what will be the tangential speed and rotational speed of his sister sitting on one of the outer horses? Conceptual Physics Chapter 10 8

Centripetal Force This In order force for must an be object totoward directed move

Centripetal Force This In order force for must an be object totoward directed move along the a circular center of path, the circle there mustitbe and is acalled forcethe acting on the centripetal force object to change itsmeans (centripetal direction of motion. “center-seeking”). Conceptual Physics Chapter 10 9

Centripetal Force ¤ The sideways acting friction between the tires of a car and

Centripetal Force ¤ The sideways acting friction between the tires of a car and the road keeps the car moving safely along a circular curve. ¤ The car door exerts an inward normal force on the passenger in a vehicle that is rounding a left-hand turn. Conceptual Physics Chapter 10 10

Centripetal Force If the road is slick or friction is not great enough, the

Centripetal Force If the road is slick or friction is not great enough, the car will have a tendency to skid off tangent to the curve. Conceptual Physics Chapter 10 11

Centripetal Force The earth exerts an inward gravitational force on the moon as it

Centripetal Force The earth exerts an inward gravitational force on the moon as it travels along its circular orbit about the earth. Conceptual Physics Chapter 10 12

Centripetal Force ¤ The spinning drum in a washing machine exerts an inward force

Centripetal Force ¤ The spinning drum in a washing machine exerts an inward force on the clothes inside of it. ¤ The holes in the spinning drum prevent it from exerting an inward force on the water and the water will consequently fly off tangent to the drum wall. Conceptual Physics Chapter 10 13

Centripetal Force Txconical A Only The Since isvector two thenet forces pendulum bob T

Centripetal Force Txconical A Only The Since isvector two thenet forces pendulum bob T force can doesn’t act beon isona bob–the resolved accelerate the bob: held mg, into in vertically, a centripetal the circular twoforce pathnet due perpendicular the force! to bygravity, force a string inand the. T, attached tension components, vertical in direction above. the. Tstring. is x The string Therefore (horizontal), zero. of a conical and TTyy pendulum (vertical). must be equal sweeps andout a cone. opposite to mg. Conceptual Physics Chapter 10 14

Centripetal Force The vertical Skidding Suppose Only two the is forces reduced component speed

Centripetal Force The vertical Skidding Suppose Only two the is forces reduced component speed actof onthe high-speed the ofvehicle the vehicle, normal isroads the by banking such weight, force that nymg, isthe equal the and vehicle turns. the andnormal opposite has Thisnoforce istendency called to mg, n (the and superelevation. to support the slide horizontal down forcethe of component The the curve inward road orof surface). upcomponent thenormal curve. of force nnormal is theforce centripetal adds toforce friction thatin to At the that friction plays no role x speed, create keeps the athe greater vehicle centripetal in on a circular force. path. keeping vehicle the track. Conceptual Physics Chapter 10 15

Centripetal Force ¤ The centripetal force prevents an object from continuing along a straight

Centripetal Force ¤ The centripetal force prevents an object from continuing along a straight line. When ¤ There is no centrifugal (outward) force! the centripetal force vanishes or is reduced, the object will fly off tangent to the circular path. Conceptual Physics Chapter 10 16

Centripetal Force ¤ Centripetal force is not a new type of force. It is

Centripetal Force ¤ Centripetal force is not a new type of force. It is any force that happens to cause an object to move along a circular path. It can be provided by gravity, friction, tension, normal force, electrical force or any combination of these. Conceptual Physics Chapter 10 17

Centripetal Acceleration ¤ Since a body undergoing uniform circular motion maintains a constant speed,

Centripetal Acceleration ¤ Since a body undergoing uniform circular motion maintains a constant speed, we must find the acceleration of this body using v 2 ac = r ¤ This is called the centripetal acceleration. Conceptual Physics Chapter 10 18

Centripetal Acceleration ¤ The centripetal acceleration and the centripetal force are related by Newton’s

Centripetal Acceleration ¤ The centripetal acceleration and the centripetal force are related by Newton’s second law: Fc = mac ¤ Both the force that causes circular motion and the acceleration that results will always be directed inward. Conceptual Physics Chapter 10 19

Centripetal Acceleration Although the speed of an object undergoing uniform circular motion remains constant,

Centripetal Acceleration Although the speed of an object undergoing uniform circular motion remains constant, the body accelerates. The velocity and acceleration vectors are always perpendicular to each other. Conceptual Physics Chapter 10 20

Centripetal Force This string Suppose The same a spinning ladybug pulls is placed inward

Centripetal Force This string Suppose The same a spinning ladybug pulls is placed inward motion on can inthe be thecan used bottom and to generate the of bottom a acan of being the simulated can whirled pulls gravity inward in a circle. on in space. the feet of the ladybug. Conceptual Physics Chapter 10 Centripetal Force 21

Simulated Gravity Even though a space station may be in free fall, the occupants

Simulated Gravity Even though a space station may be in free fall, the occupants of the space station feel a simulated gravity from the spinning motion. At the correct rotational speed this microgravity will feel identical to the gravitational pull on earth. Conceptual Physics Chapter 10 22

Simulated Gravity Space stations can either be of a modest radius with a rather

Simulated Gravity Space stations can either be of a modest radius with a rather large rotational speed or could be larger to allow for a reduced rotational speed. Conceptual Physics Chapter 10 23

Simulated Gravity Theproduce To effect of a the rotational gravity simulated speed that could

Simulated Gravity Theproduce To effect of a the rotational gravity simulated speed that could be varies directly acclimated with to by the distance most humans, from the axis spaceand station with the would havespeed rotational to be of nearly the space 2 km station. in diameter. Conceptual Physics Chapter 10 24

Question How would one’s weight be affected if the earth were to begin spinning

Question How would one’s weight be affected if the earth were to begin spinning faster on its axis? Conceptual Physics Chapter 10 25