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)

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. The mass makes 20 swings in 10 seconds. Determine the period of the mass Determine the circular speed of the mass.

II. Centripetal Acceleration Definition: Centripetal – directed toward the center (center seeking)

II. Centripetal Acceleration B. Centripetal Acceleration Equation (in reference tables): v2 a = r c 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. Determine the period of the mass. B) Determine the circular speed. C) Determine the centripetal acceleration.

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

III. Centripetal Force

v2 a = r Equation (in ref. tabs.): Fc = mac v2 Fnet = Fc = mac = m r III. Centripetal Force Equation (in ref. tabs.): Fc = mac v2 Fnet = Fc = mac = m r v2 a = r

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:

III. Centripetal Force 1. Friction: traction between road and tires 2. Gravity: Earth orbiting the Sun 3. Tension: swinging ball around on a string Normal Force: Motorcycle in steel cage (video) - Simulate Gravity (2001 video clip) Extreme G’s – Centrifuge (4 min)

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?

IV. Why do you feel a push 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

V. Forces Acting on a car going around a Corner Free- Body Diagram Fc =Ff FN Ff Fg STATIC friction is the centripetal force in this case 17

VI. 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. 18

VI. Universal Law of Gravitation The gravitational force between two objects is INVERSELY PROPORTIONAL to the square of their separation distance. 19

VI. Universal Law of Gravitation ATTRACTIVE TWO Gravity is an ________________ force between _____ objects due to their ___________ MASSES Cavendish: (1766) See Reference Tables 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 20

VI. Universal Law of Gravitation Example: 1. With what gravitational force does Earth pull on the moon? 21

VI. 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) 22

VII. Gravitational Fields WHAT IS A FORCE FIELD? Gravitational Field: A region in space where an object would experience a gravitational force Gravitational fields surround all things that have a mass. 23

VII. Gravitational Fields Gravitational Field Strength: Gravitational Field gets smaller the farther you are away Earth g g g Gravitational field strength always exists and is always constant. It exists whether there is an object there or not 24

VII. 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? 25

VIII. Weight Weight is also known as Force due to Gravity Vector quantity (magnitude and direction) Equation: Fg = mg 26

VIII. Weight 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) 10.95 m/s 27

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) 28

IX. 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 29