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Circular motion Angular Velocity V = 2πr/T V = 2πfr ω = 2πf V = rω So what direction is the force Centripetal force A rider in a “barrel of fun” finds herself stuck with her back to the wall. Which diagram correctly shows the real forces acting on her? A particle is moving in a circular path. If the force on the particle would suddenly vanish (string cut) in which direction would the ball fly off? Angus rotates a stone that is attached to the end of a cord at constant speed (counterclockwise). a. Which way is the stone accelerating? b. In which direction is the net force on the stone? c. In which direction is the ball traveling when it is right in front of him? d. If he lets the stone go in c, in which direction would it fly off? e. What effect does the string’s tug have on the stone? The force depends upon; •Mass •Radius •velocity Centripetal force F=m r a= 2 v 2 v r Note that the centripetal force is proportional to the square of the velocity, implying that a doubling of speed will require four times the centripetal force to keep the motion in a circle. If the centripetal force must be provided by friction alone on a curve, an increase in speed could lead to an unexpected skid if friction is insufficient. Also, F = 2 mr Jeff Gordon leads his race and must drive into a curve at top speed to win it all. a. What limits the speed at which he can negotiate the curve? b. If he goes into a curve of 200 m radius with a speed of 100 m/s, what centripetal acceleration does he experience? What is the acceleration of your room? This is not an idle puzzle. Copernicus argued the earth orbits the sun. On the other side Aristotle, Ptolemy and many others believed that the sun must go around the earth, because they did not feel the motion of the earth. Who is correct? We do not feel constant velocity (try closing your eyes on a smooth train or plane ride), but we do feel accelerations, both by the forces on us that cause accelerations and by the forces acting in the middle ear when the head accelerates. So, what is your acceleration due to the rotation and orbital motion of the Earth? You will need to know some values: the period of the Earth's rotation is (slightly less than) 24 hours. The actual value depends on your latitude, but your distance from the Earth's axis is not greater than six thousand kilometres. So What is the acceleration due to the Earth's rotation about its axis? To get an idea whether you would feel this, you could express your answer as a fraction of g. You should do a similar calculation for the acceleration due to the Earth's orbit, which has a radius of 1.5 x 1011 m. London eye A big wheel Slow Zodiac Fast