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Today s Objectives Rotational Motion After today, you should be able to: Recognize uniform circular motion Identify force(s) that causes circular motion Determine both tangential and centripetal acceleration Relate to gravity Practice: 7.15, 7.17, 7.21, 7.23, 7.25, 7.29, 7.31, 7.33, 7.35
NOTE: The acceleration in this case in linear acceleration, a, not angular acceleration, α
Centripetal Force Newton s 1 st Law: An object in motion will stay in motion with constant speed and direction unless acted on by an external force. A centripetal force is the force that makes an object move in a curved path. The can moves in a circle because of the tension in the rope The force exerted radially inward by friction on the tires makes the car move in a circle.
Contrast with Centrifugal Force (A Fictitious Force) Centrifugal: The faster you go, it feels like there is an increasing force pushing you away from the center of the merry-go-round. Centripetal: In reality, your body is trying to follow Newton s first law, but the merry-goround is applying a force to go in a circle.
The merry go round is turning clockwise as viewed from the top, as shown. If you are standing on the bottom edge (boundary between red and yellow), what direction would you go if you let go? A B E C D Q8
Fictitious Forces (Centrifugal Force) According to Newton s 1 st Law, your body wants to continue to move in a straight line of constant velocity and if you don t hold on or hold yourself against a bar (adding a centripetal force), you will move in a straight line off the merry-go-round.
Circular Motion in Merry Go Rounds Watch after class: https://www.youtube.com/watch?v=zhpaifn_2sw Watch in class: https://www.youtube.com/watch?v=ewx4iapbees
Newton s Laws Appear Like They Don t Work From An Accelerating Reference Frame (with respect to the ground, they do)
(ΣF = ma) a a tan a R
Relations Between Angular and Linear Quantities If w is increasing or decreasing, there is a tangential acceleration in addition to the centripetal acceleration v rw a tan v t ( rw) t r w t Note that net acceleration is a r tan v r (wr) r 2 2 a R a a 2 R w r a a tan R
What kind of acceleration does a person at the equator of Earth experience due to Earth s rotation about its axis? A. Tangential/Angular B. Centripetal/Radial C. Neither D. Both Q9
The Earth is not speeding up, so the tangential acceleration a tan =0=r The radial acceleration a radial =v 2 /R
Artificial gravity Astronauts spending lengthy periods of time in space experience negative effects due to weightlessness, such as weakening of muscle tissue. In order to simulate gravity, how many revolutions per minute would be required to create a normal force equal in magnitude to the astronaut's weight? 50m
Same Idea for a Centrifuge A sample of blood is placed in a centrifuge of radius 16.0 cm. The mass of a red blood cell is 3.0 x10-16 kg, and the magnitude of the force needed to make it separate from the plasma is 4.0 x 10-11 N. At how many revolutions per second should the centrifuge be operated?
Do you think Spiderman s spider silk could hold up? Consider Spiderman swinging off Let s assume Spider-Man starts from rest, of the top has of only a building potential 15 energy. m tall. At the bottom of his swing, he has only kinetic energy (K = ½mv 2 ). To find Spider-Man's velocity at the bottom of his swing, we apply the law of conservation of energy. Therefore: ½mv 2 = mgh Solving for v gives: v = sqrt(2gh) = sqrt(2(9.8 m/s 2 )(15 m)) = 17.15 m/s The velocity at the bottom of his swing is 17.15 m/s (38.36 mph). In order to calculate the tension in Spider-Man's web, we use: ΣF radial =ma radial =mv 2 /r = T mg (r is the radius of the circle formed while Spider-Man swings) We solve for T, and find that T = mv 2 /r +mg = (68 kg)(17.15 m/s) 2 /(15 m)+(68 kg)(9.8 m/s 2 ) = 2000 N!
It s true! Spider silk could stop a Boeing 747 in flight, is stronger than bullet-proof Kevlar and more elastic than nylon, biologists say.
Why does the Moon Orbit the Earth? All objects that have mass attract each other Magnitude of gravitational attractive force between two objects is related to the masses and distance between them. m1m F G G 2 r r = distance between centers of two objects G = 6.67 10-11 N m 2 / kg 2 (Gravitational Constant) 2
A. B. C. D. Q10
A. B. C. D. E. Q11
A. B. C. D. E. Q12
A DVD is rotating with an ever-increasing speed. How does the centripetal acceleration a rad compare at points P and Q? A. P and Q have the same a rad B. Q has a greater a rad than P. C. Q has a smaller a rad than P. Q13
Good Summary http://www.youtube.com/watch?v=- G7tjiMNVlc
Chapter/Section: Clicker #=Answer Ch.7: 8=B, 9=B,