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Circular motion 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? A scientist is completely isolated in a box moving smoothly through space in a straight line. Another scientist is in a similar box spinning smoothly in space. Each scientist can have anything she needs to detect motion. Which scientist can detect her motion? 1. The first box 2. The spinning box 3. Both 4. Neither See p 105 Circular Motion A cat runs across the floor from A to B to C without changing its speed. Can we say for sure that a force has acted on the cat at B? B A a. Yes, there had to be a force on the cat at B b. Not necessarily, as the cat’s speed has not changed See p107 C Circular Motion • An object will not move, or it will stay at a constant speed if there is no resultant force acting on it. • When an object moves at a constant speed in a circle its direction constantly changes, so there must be a force acting inwards to stop it flying away • This force is called the centripetal force • When this force is removed the object will fly off in a straight line An object moving in a circle requires a centripetal force acting inwards Centripetal Acceleration • Remember that acceleration = change in velocity • Velocity is a vector (speed in a given direction), so acceleration occurs if speed or direction change • An object turning has a changing direction, so even if its speed is constant its velocity must be changing and it must be accelerating • The centipetal force causes centripetal acceleration towards the centre of the circle m v F v F m What variables increase the force needed? Imagine spinning a mass around your head • As the mass of the object increases the centripetal force you need to stop it flying off increases • As the speed of the object increases the centripetal force you need to stop it flying off increases • But as the length of the string* increases the force you need to stop it flying off decreases * Radius of the circle What provides the centipetal force? • The force is obvious when there’s tension through a string (or handle) as in the hammer throw, but less obvious without one video • For cars going around bends centripetal force comes from friction between the tyres and the road. Without friction a car will skid off in a straight line • How does banking on a racetrack help? • What provides the centripetal force for satellites? A centrifuge is used to separate heavy things in suspension from lighter things, such as blood cells from the plasma • As the mass of the object increases the centripetal force you need to stop it flying off increases • So at a certain speed the centrifugal force will hold lighter objects in the liquid but will not be strong enough to stop the heavier ones from moving outwards to the end of the test tube. Circular motion 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? A scientist is completely isolated in a box moving smoothly through space in a straight line. Another scientist is in a similar box spinning smoothly in space. Each scientist can have anything she needs to detect motion. Which scientist can detect her motion? 1. The first box 2. The spinning box 3. Both 4. Neither See p 105 Circular Motion A cat runs across the floor from A to B to C without changing its speed. Can we say for sure that a force has acted on the cat at B? B A a. Yes, there had to be a force on the cat at B b. Not necessarily, as the cat’s speed has not changed See p107 C Circular Motion • An object will not move, or it will stay at a constant speed if there is no resultant force acting on it. • When an object moves at a constant speed in a circle its direction constantly changes, so there must be a force acting inwards to stop it flying away • This force is called the centripetal force • When this force is removed the object will fly off in a straight line An object moving in a circle requires a centripetal force acting inwards Centripetal Acceleration • Remember that acceleration = change in velocity • Velocity is a vector (speed in a given direction), so acceleration occurs if speed or direction change • An object turning has a changing direction, so even if its speed is constant its velocity must be changing and it must be accelerating • The centipetal force causes centripetal acceleration towards the centre of the circle m v F v F m Uniform Circular Motion An object rotating at steady speed A r If the frequency = f and period = T What is the speed of A? Angular Displacement and Angular Speed Angular displacement θ is the angle in radians through which an object has rotated in time t θ = t/T x 2π = 2πft in rads Angular speed per second ω (omega) is the angular displacement ω = θ/t = 2π/T = 2πf What is the unit? r ϴ ω = 2π/T = 2πf s If length of the arc = s s = vt = 2πr/T x t = 2πrt/T As θ = 2πt/T s = θr And the speed of rotation of the object v = 2πr/T = ωr (see p23) Centripetal force Loop the Loop: https://www.youtube.com/watch?v=wiZoVAZGgsw&feature= youtube_gdata_player See also Indian wall of Death 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? The force depends upon; •Mass •Radius •velocity Centripetal force F=m r a= 2 v 2 v r So what is the force on a sock in a spin drier? 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 m r 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 lift F A banked turn Bigger F