# Centripetal force keeps an object in circular motion Rotation and Revolution

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1 Centripetal force keeps an object in circular motion Rotation and Revolution Two types of circular motion are and. An is the straight line around which rotation takes place. When an object turns about an internal axis that is, an axis located within the body of the object the motion is called, or spin. When an object turns about an external axis, the motion is called. 1

2 10.2 Rotational Speed The turntable around its axis while a ladybug sitting at its edge - around the same axis Rotational Speed Types of Speed is the distance traveled per unit of time. A point on the outer edge of the turntable travels a greater distance in one rotation than a point near the center. The is greater on the outer edge of a rotating object than it is closer to the axis. The speed of something moving along a circular path can be called because the direction of motion is always tangent to the circle. 2

3 Linear Speed Example Curtis favorite disco record has a scratch 12 cm from the center that makes the record skip 45 times each minute. What is the linear speed of the scratch as it turns? 10.2 Rotational Speed (sometimes called angular speed) is the number of rotations per unit of time. All parts of the rigid turntable rotate about the axis in the same amount of time. All parts have the same, or the same number of rotations per unit of time. It is common to express rotational speed in revolutions per minute (RPM). 3

4 10.2 Rotational Speed All parts of the turntable rotate at the same speed. a. A point farther away from the travels a longer path in the same time and therefore has a greater speed. b. A ladybug sitting twice as far from the center moves as fast Rotational Speed Tangential and Rotational Speed Tangential speed and rotational speed are related. Tangential speed is directly proportional to the rotational speed and the radial distance from the axis of rotation. Tangential speed ~ - In symbol form, v ~ r You move if the rate of rotation increases (bigger ). You also move if you are farther from the axis (bigger r). 4

5 10.2 Rotational Speed think! At an amusement park, you and a friend sit on a large rotating disk. You sit at the edge and have a rotational speed of 4 RPM and a linear speed of 6 m/s. Your friend sits halfway to the center. What is her rotational speed? What is her linear speed? 10.3 Centripetal Force The centripetal force on an object depends on the object s, its, and the of its circular path. 5

6 10.3 Centripetal Force Velocity involves both speed and direction. When an object moves in a circle, even at constant speed, the object still undergoes because its direction is changing. This change in direction is due to a net force (otherwise the object would continue to go in a straight line). Any object moving in a circle undergoes an acceleration that is directed to the center of the circle a. Example 1 A 150 kg ball at the end of a string is revolving uniformly in a horizontal circle of radius m. The ball makes 2.00 revolutions in a second. a) What is the tangential speed? b) What is the centripetal acceleration? 6

7 Example 2 Missy s favorite ride at the Topsfield Fair is the rotor, which has a radius of 4.0 m. The ride takes 2.0 s to make one full revolution. a) What is Missy s linear speed on the rotor? b) What is Missy s centripetal acceleration on the rotor? 10.3 Centripetal Force means toward the center. The force directed toward a fixed center that causes an object to follow a circular path is called a centripetal force. 7

8 10.3 Centripetal Force Centripetal force is not a basic force of nature, but is the label given to that is directed toward a fixed center. If the motion is circular and executed at constant speed, this force acts at right angles (tangent) to the path of the moving object Centripetal Force holds a car in a curved path. a. For the car to go around a curve, there must be sufficient friction to provide the required centripetal force. b. If the force of friction is not great enough, skidding occurs. 8

9 10.3 Centripetal Force The clothes in a washing machine are forced into a circular path, but the water is not, and it flies off Centripetal Force Calculating Centripetal Forces Greater speed and greater mass require greater centripetal force. Traveling in a circular path with a smaller radius of curvature requires a greater centripetal force. Centripetal force, F c, is measured in newtons when m is expressed in kilograms, v in meters/second, and r in meters. 9

10 10.3 Centripetal Force 10

11 10.4 Centripetal and Centrifugal Forces The is attributed not to any real force but to inertia the tendency of the moving body to follow a straightline path. Example 1 Captain Chip, the pilot of a 60,500-kg jet plane, is told that he must remain in a holding pattern over the airport until it is his turn to land. If Captain Chip flies his plane in a circle whose radius is 50.0 km once every 30.0 min, what centripetal force must the air exert against the wings to keep the plane moving in a circle? 11

12 10.4 Centripetal and Centrifugal Forces Sometimes an outward force is also attributed to. This apparent outward force on a rotating or revolving body is called. Centrifugal means center-fleeing, or away from the center Centripetal and Centrifugal Forces When the string breaks, the whirling can moves in a straight line, tangent to not outward from the center of its. 12

13 10.4 Centripetal and Centrifugal Forces The only force that is exerted on the whirling can (neglecting gravity) is directed toward the center of circular motion. This is a force. No outward force acts on the can Centrifugal Force in a Rotating Reference Frame is an effect of rotation. It is not part of an interaction and therefore it cannot be a true force. 13

14 An object will remain in rotational equilibrium if its center of mass is above the area of support. What determines whether an object will rotate when a force acts on it? Why doesn t the Leaning Tower of Pisa rotate and topple over? What maneuvers does a falling cat make to land on its feet? This chapter is about the factors that affect 14

15 11.1 Torque To make an object turn or rotate, apply a Torque Every time you open a door, turn on a water faucet, or tighten a nut with a wrench, you exert a turning force. is produced by this turning force and tends to produce rotational acceleration. Torque is different from force. 15

16 11.1 Torque When a is applied, the lever arm is the distance between the doorknob and the edge with the hinges Torque When the force is perpendicular, the distance from the turning axis to the point of contact is called the lever arm. If the force is not at right angle to the lever arm, then only the perpendicular component of the force will contribute to the torque. 16

17 11.1 Torque Although the magnitudes of the are the same in each case, the are different Torque think! If you cannot exert enough torque to turn a stubborn bolt, would more torque be produced if you fastened a length of rope to the wrench handle as shown? 17

18 Example Torque A water faucet is turned on when a force of 2.0 N is exerted on the handle, at a distance of m from the pivot point. How much torque must be produced to turn the handle? 11.2 Balanced Torques When balanced torques act on an object, there is no change in rotation. 18

19 11.2 Balanced Torques A pair of torques can each other. Balance is achieved if the torque that tends to produce clockwise rotation by the boy equals the torque that tends to produce rotation by the girl Balanced Torques do the math! What is the weight of the block hung at the 10-cm mark? 19

20 11.2 Balanced Torques do the math! The block of unknown weight tends to rotate the system of blocks and stick counterclockwise, and the 20-N block tends to rotate the system clockwise. The system is in balance when the two torques are equal: counterclockwise torque = clockwise torque Mabel and Maude are seesawing on the school playground and decide to see if they can move to the correct location to make the seesaw balance. Mabel weighs 400. N and she sits 2.00 m from the fulcrum of the seesaw. Where should 450.-N Maude sit to balance the seesaw? 20

21 11.3 Center of Mass The center of mass of an object is the point located at the object s of mass Center of Mass A baseball thrown into the air follows a smooth parabolic path. A baseball bat thrown into the air does not follow a smooth path. The bat wobbles about a special point. This point stays on a parabolic path, even though the rest of the bat does not. The motion of the bat is the sum of two motions: a spin around this, and a through the air as if all the mass were concentrated at this point. This point, called the, is where all the mass of an object can be considered to be concentrated. 21

22 11.3 Center of Mass The centers of mass of the baseball and of the spinning baseball bat each follow parabolic paths Center of Mass Location of the Center of Mass For a symmetrical object, such as a baseball, the center of mass is at the of the object. For an irregularly shaped object, such as a baseball bat, the center of mass is toward the end. 22

23 11.3 Center of Mass The center of mass of the toy is below its geometric center Center of Gravity For everyday objects, the center of gravity is the same as the center of mass. 23

24 11.5 Torque and Center of Gravity If the center of gravity of an object is above the area of support, the object will remain upright Torque and Center of Gravity The block topples when the CG extends beyond its support base. 24

25 11.5 Torque and Center of Gravity The Rule for Toppling If the CG extends outside the area of support, an unbalanced torque exists, and the object will topple. The Leaning Tower of Pisa does not topple because its does not extend beyond its base. A vertical line below the CG falls inside the base, and so the Leaning Tower has stood for centuries. If the tower leaned far enough that the CG extended beyond the base, an unbalanced torque would topple the tower Center of Gravity of People The center of gravity of a person is not located in a fixed place, but depends on body orientation. Center of Gravity Activities 25

26 11.6 Center of Gravity of People think! When you carry a heavy load such as a pail of water with one arm, why do you tend to hold your free arm out horizontally? Rotating objects tend to keep rotating while nonrotating objects tend to remain non-rotating. 26

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