PHY 101 1nd Edition Lecture 20 Outline of Last Lecture I 7 2 Rotational Motion Under Constant Angular Acceleration II 7 3 Angular Linear Quantities a Tangential Speed Acceleration III 7 4 Centripetal Acceleration a Centripetal Tangential Acceleration Outline of Current Lecture IV Summary Angular Linear Quantities V Forces Causing Centripetal Acceleration VI Problem Solving Strategies VII 7 5 Newtonian Gravitation Revisited Current Lecture Example Discus Throw A discus thrower turns with an angular acceleration of a 50rad s2 Find the magnitude of the total acceleration and tangential speed when he reaches an angular speed of 10 rad s Note the total acceleration a at2 ac2 1 2 Solution find centripetal acceleration o At r 0 8 50 40m s2 o A 40 2 80 2 1 2 89 m s 2 Summary Angular Linear Quantities When a rigid object rotates o The arc length linear distance s r o The velocity is ltangential to its trajectory o Tangential speed v r o Tangential acceleration at r o Centripetal acceleration ac vt2 r Forces Causing Centripetal Acceleration These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Even an object is doing a constant speed circular motion it experiences a centripetal acceleration ac According to Newton s 2nd law any acceleration is accompanied by a force in this case o Fc mac ac v2 r r The force is also called centripetal force Examples of centripetal force o Tension in a string o Gravity o Force of friction Centripetal Force Examples Whirling a ball of mass m with a string the tension T of the string provides the centripetal force o The faster the ball moves the greater the tension o T mac mv2 r Car travelling along a circular track friction provides centripetal force o Fs mac mv2 r o dangerous to make a sudden turn while the car is moving at high speeds especially on icy roads o the friction may not be enough to provide the needed centripetal force The car may be out of control example o the gravitational forces between planets the sun provide the centripetal force for their circular motions around the sun o Fg Fc o Fg Gm1m2 r2 Fc mv2 r o Gm1m2 r2 mv2 r o Gm2 r v2 The closer the planet is to the sun the faster it is orbiting Problem Solving Strategy Draw free body diagram showing and labeling all the forces acting on the object s Choose a coordinate system that has one axis perpendicular to the circular path and the other axis tangent to the circular path Find the net force toward the center of the circular path this is the force that causes the centripetal acceleration Fc Use Newton s 2nd law o The directions will be radial normal and tangential o The acceleration in the centripetal acceleration Solve for the unknowns 7 5 Newtonian Gravitation Revisited Newton s law of universal gravitation o Fg Gm1m2 r2 On earth s surface the weight of an object with a mass m is o Fg mg GmMg Re2 g GMe Re2 The gravitational acceleration g will vary with altitude Gravitational PE Pe mgy is only valid near the Earth s surface o In this case the reference point is chosen as Earth s surface For object s high above the Earth s surface an alternate expression is needed o PE GMem r o Zero reference level is infinitely far from the Earth s surface On Earth s surface the PE of the Earth object system is o PE GMem r
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