Unit 5: Gravity and Rotational Motion
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10/1/19 1 Unit 5: Gravity and Rotational Motion Brent Royuk Phys-109 Concordia University 2 Rotational Concepts • There’s a whole branch of mechanics devoted to rotational motion, with angular equivalents for distance, speed, acceleration, mass, force, momentum and energy. • Angular Speed, ω is measured in degrees (or radians) per second, not meters per second. • Rotational Inertia, I depends on shape as well as mass, and measures how hard it is to rotate something. • The rotational equivalent for force is Torque, τ which is a twisting force that depends on how hard you apply a force and how far away from the rotational axis you push. – Torque = force x lever arm 3 Rotational Concepts • Angular Momentum, L is a conserved quantity. Lb = La Ibωb = Iaωa • Pulling string while bob rotates • Spinning skaters • Rotating platform
Transcript of Unit 5: Gravity and Rotational Motion
10/1/19
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Unit 5: Gravity and Rotational
MotionBrent Royuk
Phys-109Concordia University
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Rotational Concepts• There’s a whole branch of mechanics devoted to rotational motion, with
angular equivalents for distance, speed, acceleration, mass, force, momentum and energy.
• Angular Speed, ω is measured in degrees (or radians) per second, not meters per second.
• Rotational Inertia, I depends on shape as well as mass, and measures how hard it is to rotate something.
• The rotational equivalent for force is Torque, τ which is a twisting force that depends on how hard you apply a force and how far away from the rotational axis you push.– Torque = force x lever arm
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Rotational Concepts• Angular Momentum, L is a conserved quantity.
Lb = La
Ibωb = Iaωa
• Pulling string while bob rotates• Spinning skaters• Rotating platform
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Rotational Concepts• Angular Momentum, L is a conserved quantity.
Lb = La
Ibωb = Iaωa
Rotational Vectors• Gyroscopic stability
– Football spirals– Bullets
• Precession– Gyroscope– Diving airplanes– Helicopters– Motorcycle turns
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Traveling in Circles• A mass on a string
– Which way does the mass accelerate?– Which way does the force act on the mass?
• Two Latin Words– Centripetal (Center-Seeking)– Centrifugal (Center-Fleeing)
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Newton and Gravity• Another amazing scientific achievement.• 1665, 23 years old• ...in November [I] had the direct method of fluxions...in May following I had entrance
into the inverse method of fluxions. And the same year I began to think of gravity extending to the orb of the Moon...& thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age of invention & minded Mathematicks & Philosophy more than at any time since. –Newton in an unsent letter to Pierre Des Maizeaux
"The Principia is pre-eminent above any other production of human genius." —Pierre-Simon Laplace"Taking mathematics from the beginning of the world to the time when Newton lived, what he has done is much the better part." —Gottfried Leibniz"All that has been accomplished in mathematics since his day has been a deductive, formal, and mathematical development of mechanics on the basis of Newton's laws." —Ernst Mach
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The Law• Newton’s Law of Universal
Gravitation
• Whack! Isaac Newton, you’ve discovered gravity!
• What’s universal about Newton’s Universal Law of Gravitation?
• The apple and the moon– The moon is made of stuff, just
like the apple.
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Gravity• The Law:
• G = 6.67 x 10-11 N m2/kg2
• Why don’t we ever notice attractions between two terrestrial bodies?– Physical attraction on a love seat.
• “Let each person be a uniform-density sphere…”
• Big G, Little g• Mt. Everest
– gEverest = 9.78 m/s2
• Gravity is an Inverse Square Law– What if you halve the distance between objects?
• Double it?
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Gravity• gshuttle = 9.08 m/s2, 7.44% less than Earth’s
surface.
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Cavendish’s Torsion BalanceWeighing the Earth
Huh?
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Cavendish’s Torsion BalanceJohn Walker’s modern reproduction• Bending Spacetime in the Basement
– http://www.fourmilab.com/gravitation/foobar/
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Gravity and OrbitWhy are astronauts weightless in orbit?
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Projectile Motion• What path does the ball follow when
dropped?
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Projectile Motion• Horizontal Launch
– What happens if you kick a ball off a cliff?
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Projectile Motion• Falling Comparison
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Projectile Motion• Horizontal Launch
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Projectile Motion
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Projectile Motion• Maximum Range
• Estimate the range of a well-thrown baseball.
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Projectile Motion
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Projectile Motion
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Projectile Motion• Air Resistance
– Data: 100 mph at 60o; vacuum = 581 ft., air = 323 ft.
• How about the moon?
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Projectile Motion• How about the moon? Alan Shepard, Apollo 14
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Projectile Motion
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Orbits• Rocket Science
– At earth’s surface, orbital velocity would be:
– The radius of Earth is 6371 km.– The size of the satellite doesn’t matter.– 500 km above surface, 7.6 km/s.
• What makes rocket science hard?
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Satellite Orbital Height
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Geosynchronous Orbit
Height: 35786 km = 22,236 milesEarth’s radius: 6371 km = 3959 miles
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Escape Velocity• What is the escape velocity of the Earth?
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ConcepTestAstronauts appear weightless in their spacecraft because...a. They are falling at the same rate as the
spacecraft.b. There is very little gravity in space/outside
earth’s atmosphere.c. They are too far away from Earth or any
massive body.d. There is no gravity inside the spacecraft.
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Newtonian Limitations
