Unit 5: Circular Motion And Gravity

I. Uniform Circular Motion (UCM) Definition: Motion of an object traveling at a CONSTANT SPEED on a circular path Describing Circular Velocity: Always TANGENT to circle (video) (video 2)

I. Uniform Circular Motion (UCM) Period (T) – Time to travel ONCE around a circular path Circular Speed Equation: d = 2πr d V = = 2πr t T Period = T = _t_ # of cycles

I. Uniform Circular Motion (UCM) Example: A mass swings around in uniform circular motion by a string with a radius of 0.8 m. If the mass makes 20 swings in 10 seconds, what is the speed of the mass?

II. Centripetal Acceleration CENTER Centripetal means directed toward the __________

II. Centripetal Acceleration Centripetal Acceleration Equation (in reference tables): v2 a = c r m Units: s2

II. Centripetal Acceleration Example: A 5 kg mass travels in uniform circular motion connected to a string with a radius of 2 m. The mass makes 100 revolutions in 2 minutes. What is the centripetal acceleration of the mass?

III. Centripetal Force Review of Newton’s 2nd Law Equation: Fnet = ma Centripetal Force and Centripetal Acceleration: Sum of force (net force) causes centripetal acceleration Equation (in ref. tabs.): r

III. Centripetal Force Cool video (1 min)

III. Centripetal Force IMPORTANT NOTE: Centripetal force is the sum of the forces required for circular motion to occur. This “required force” is provided by some “real” force, for example: 1. Friction: traction between road and tires 2. Gravity: Earth orbiting the Sun 3. Tension: swinging ball around on a string 4. Normal Force: Simulate gravity using a centrifuge (2001 video clip)

III. Centripetal Force Example: Lance Mellon and his bike have a mass of 70.0 kg. He completes one lap in 12.2 seconds around a circular track with a radius of 10.0 m. A) List all givens and draw a free-body diagram B) Find the circular velocity of Lance

III. Centripetal Force Example: Lance Mellon and his bike have a mass of 70.0 kg. He completes one lap in 12.2 seconds around a circular track with a radius of 10 m. C) Find the centripetal acceleration D) What force must the track exert on the tires to produce this acceleration? E) What is the coefficient of friction between the tires and the road?

Why do you feel a push by the door when you are going around a corner in a car? Your body wants to travel straight (tangent to circle) Car door pushes you inward to travel in a circle

IV. Forces Acting on a car going around a Corner Fc =Ff Free- Body Diagram FN Ff Fg 14

WORK ON THIS PROBLEM WITH YOUR TABLE PARTNER IV. Forces Acting on a car going around a Corner STATIC friction is the CENTRIPETAL force in this case Example: A 2000 kg car circles a track with a radius of 45 m at a speed of 15 m/s. Find Ff and coefficient of static friction. WORK ON THIS PROBLEM WITH YOUR TABLE PARTNER 15

V. Universal Law of Gravitation Newton’s discoveries (1666) “The apple falls…” The gravitational force between two object is PROPORTIONAL to the product of their masses. 16

V. Universal Law of Gravitation The gravitational force between two objects is INVERSELY PROPORTIONAL to the square of their separation distance. 17

V. Universal Law of Gravitation Universal Law of Gravitation: Gravity is an _____________ force between _____ objects due to their ___________ ATTRACTIVE TWO MASSES Cavendish (1766) made Newton’s proportionalities an equation by deriving the Universal Gravitation Constant (G) G = universal gravitational constant = 6.67 x 10-11 N*m2/kg2 Fg = Force due to Gravity m1 and m2 = masses r = distance between two objects 18

V. Universal Law of Gravitation Example: 1. With what gravitational force does Earth pull on the moon? 19

V. Universal Law of Gravitation Example: 2. With what gravitational force does the moon pull on the Earth? Equal in magnitude (1.99 x10 20 N), but opposite in direction (Newton’s 3rd Law) 20

VI. Gravitational Fields A region in space where an object would experience a gravitational force Gravitational fields surround all things that have a mass and work over infinite distances. The field strength becomes weaker the farther away from the object creating the field and is directed toward the center of the mass. 21

VI. Gravitational Fields Earth Gravitational fields become weaker as you move farther away from the object creating the field. 22

VI. Gravitational Fields Equation: Example: A 50 kg object feels a gravitational force of 300 N when placed in the gravitational field of a planet. What is the gravitational field strength at the location of the object? 23

VII. Weight (Revisited) Weight is also known as force due to gravity Weight is the force of attraction between an object and a large body it is near (e.g. – Earth) Weight varies. depending on what the object is attracted to and its location Equation: Fg = mg 24

VII. Weight (Revisited) Deriving the acceleration due to gravity on Earth: 25

VII. Weight (Revisited) An artificial gravity centrifuge helps astronauts experience different gravities by spinning them around in a circle. If the centrifuge has a radius of 4 m, how fast does it need to spin in order to have a person experience triple the Earth’s acceleration due to gravity? Extreme G’s (centrifuge) (4 min) 10.8 m/s 26

Cool Videos Wringing Out Water Aboard the ISS (3 min) Aboard the Vomit Comet (4 min) 2001: A Space Odyssey (2 min) Extreme G’s (centrifuge) (4 min) 27

VIII. Whiteboard Problems With your partner, complete the problems on the whiteboard. Answers: 1A) 39.3 m/s, B) 62 m/s2, C) 3084 N 2A) 6.28 m/s, B) 19.7 m/s/s, C) 59.2 N 3A) 15.7 m/s, B) No, mass does not affect ac, C) Yes, different masses 4A) 4 s, B) 31.4 m/s, C) 49.3 m/s/s, D) 3701 N 5A) 6.67 m/s/s, B) 533 N, C) 0.680 6) 1.71 m/s/s 7) 9.11 x 10 -31 kg 28