An object moving in a circle with radius at speed is said to be undergoing.

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1 Circular Motion Study Guide North Allegheny High School Mr. Neff An object moving in a circle with radius at speed is said to be undergoing. In this case, the object is because it is constantly changing its direction. This acceleration is pointed toward the of the circle, and so we call it a acceleration, an adjective that means -. We know it is pointed toward the center, because acceleration always points the same way as the, which clearly points toward the center. Because this net force causes this acceleration, we call it force. Centripetal force is not the of a force; instead, it does not describe what type of object is exerting the force, like normal force(the result of a bowed surface), tension force (the result of a stretched string) or friction (the result of sliding of two irregular surfaces), among others. Rather, the word centripetal on a force tells that the force is directed toward the center of the circle. A good description of a centripetal force will have both the word centripetal and the name of the force, like centripetal tension force (for a string pulling an object in a circle), centripetal gravitation force (for a satellite being pulled in a circular orbit), or a centripetal friction force (allowing a car to round a corner). Some people also think objects in uniform circular motion also experience an outward force. This is an. When an object moves in a circle, its inertia causes it to resist changes in its state of motion. Consequently, the object attempts to (and will, without enough centripetal force) move to the outside of the circle. When the moving object is a person, this inertial effect is easily misinterpreted as a force to the outside, or a centrifugal force. Centripetal acceleration depends on the of the object s speed and on the radius of the circle. Elegantly, a c = To get centripetal force from centripetal acceleration, simply multiply by the. The of a rotating object is the time it takes to complete one rotation or make one complete cycle. It is generally measured in. The of a rotating object is the number of complete rotations or cycles completed in a time interval, usually, in which case the unit is rotations/second or. The relationship between period and frequency is that they are.

2 is the rate of change of the angle of the rotating object. The central angle is the angle with its at the center of the circle. The symbol for angular velocity is the, and it is usually measured in per. What is the direction of the force that acts on the clothes in the spin cycle of a washing machine? What exerts the force? You are sitting on the back seas of a car that is going around a curve to the right. Sketch a diagram to answer the following questions. a. What is the direction of your acceleration? b. What is the direction of the net force acting on you? c. What exerts the force on you? Thanks to Earth s daily rotation, you always move with uniform circular motion. What supplies the force that accelerates you? How does this motion affect your apparent weight, that is, how would your weight be affected if the Earth stopped rotating?

3 A 13-gram rubber stopper is attached to a string, making a horizontal circle of radius 0.93-m. The stopper makes one revolution in 1.18 seconds. Find the tension exerted by the string on the stopper. Racing on a flat track, a car going 32 m/s rounds a curve 56 m in radius. a. What is the car s centripetal acceleration? b. What minimum coefficient of static friction between the tires and the road would be needed for the car to round the curve without slipping?

4 Early skeptics of the idea of a rotating Earth said that the fast spin would throw people off at the equator into space. The radius of the Earth is about 6.37 x 10 6 m. Show why this objection is wrong by calculating: a. the speed of a 97-kg person at the equator b. the force needed to accelerate the person in the circle c. the weight of the person d. the normal force of earth on the person, that is, the person s apparent weight The carnival ride shown to the right has a radius of 2.0 m and rotates once each 0.90 seconds. a. Find the speed of the rider b. Find the centripetal acceleration of the rider c. What produces this acceleration? d. How does the rider interpret this acceleration? e. Is the ride spinning fast enough to safely get completely vertical? f. What is the coefficient of static friction between the riders and the walls if the floor could be dropped out when the ride is perfectly horizontal?

5 A 65-kg circus carnie is sitting on a steadily-rotating Ferris wheel with a radius of 5.5 meters. The standard 5 minute ride gives the rider 12 full trips around the circle. a. What is the carnie s apparent weight at the top of the ride? b. What is the carnie s apparent weight at the bottom of the ride? c. What is the carnie s apparent weight at the middle of the ride? d. How fast would the ride have to rotate to give the carnie a weightless feeling at the top of the ride? In 1665, at the age of 23, Isaac Newton showed that, the force that makes apples fall to the Earth, is the same force that makes the moon orbit the Earth. Not only does Earth attract apples and moons, but every body in the universe attracts every other body. This tendency of bodies to move toward each other is called. Quantitatively, Newton proposed a force law that we now call Newton s Law of Universal Gravitation: every particle attracts every other particle with a gravitational force whose magnitude is given by:

6 Here, G is the. Its value is now known to be. The direction of the gravitational force is directed toward the center of. Using this important equation, Henry Cavendish the Earth in He set up an experiment in which he used the small gravitational attraction between two large spheres to twist a delicate wire a small amount. From this twisting, Cavendish was able to fill in everything but the G in Newton s equation. Once he calculated G, Cavendish was able to determine the mass of the Earth! A satellite orbits Earth 225 km above its surface. What is its speed in orbit and its period? The sun is considered to be a satellite of our galaxy, the Milky Way. The sun revolves around the center of the galaxy with a radius of 2.2 x m. The period of one revolution is 2.5 x 10 8 years. a. Find the mass of the galaxy. b. Assuming the average star in the galaxy has the same mass as the sun, find the number of stars. c. Find the speed of which the sun moves around the center of the galaxy.

7 Friction provides the force needed for a car to travel around a flat, circular track. What is the maximum speed at which a car can safely travel if the radius of the track is 80.0 m and the coefficient of friction is 0.40? A banked curve uses normal force to get a car around a turn rather than relying solely on friction. If a curve with radius of 30 m is banked at an angle of 42º, for what speed is this curve rated?

8 constant (fixed) constant uniform circular motion accelerating center centripetal center-seeking net force centripetal name centrifugal illusion directly square inversely a c = v 2 /r mass period seconds frequency one second hertz reciprocals angular velocity central vertex ω radians second The force is toward the center of the tub. The walls of the tub exert the force on the clothes. Of course, the whole point is that some of the water in the clothes goes out through the holes in the wall of the tub moving toward the center. ANSWERS 18 m/s/s m/s 3.3 N N m/s 97.5m/s/s Normal Force of Walls As a centrifugal force pushing them outward Yes, 4.4 m/s/s < 14 m/s/s N N N 7.34 m/s gravity gravitation F g = m 1 m 2 /r 2 Universal Gravitation Constant 6.67 x N kg 2 /m 2 the object exerting the gravitational force weighed 7780 m/s 88.8 minutes 1.0 x kg 5.0 x x 10 5 km/h 18 m/s a. Your body is accelerated to the right. b. The net force acting on your body is to the right. c. The force exerted by the car s seat and maybe the door to your left. 16 m/s ( 36 mph) Earth s gravity supplies the force that accelerates you in circular motion. Your uniform circular motion decreases your apparent weight (.36 Rad) above horizontal