PHYS 1111 1nd Edition Final Exam Study Guide Chapter 9 4 9 7 Collisions Center of Mass Impulse I F t p Ns Linear momentum p mv Ns Collision 2 or more objects whose motion velocity or momentum is altered by collision o Conservation of linear momentum pf pi Elastic collision energy momentum conserved v f v i ex Boy jumps and misses raf o Inelastic collision momentum conserved but energy is not conserved ex Boy jumps and lands on raf Center of Mass point where system can be balanced in a uniform gravitational field o x cm m1 x 1 m2 x 2 m1 m2 o v cm m1 v 1 m 2 v 2 m1 m 2 o acm m1 a1 m 2 a2 m1 m 2 Zero net external force if an object is at rest it remains at rest and if an object is moving it continues moving Thrust force exerted on rocket by ejected fuel Thrust m v t Example If a car with mass 760 kg is travelling east at a speed of 10 m s hits a wall and rebounds west with a velocity of 0 1 m s what s its momentum before and afer impact Determine the impulse o pi mv 760 10 7500 Ns o pf mv 760 0 1 75 Ns o I pf pi 75 7500 7575 Ns Chapter 10 Rotational Kinematics 1 revolution 360 degrees 2pi radians Angular velocity rad s t Tangential velocity v r r 2 T Period time to complete 1 revolution T Average Angular Acceleration 2 s rad s t Centripetal Acceleration acp r 2 Tangential Acceleration aT r Translational Kinetic Energy 1 m v 2 vs Rotational Kinetic Energy 2 1 I 2 2 Example A thin rigid rod rotates with a constant angular acceleration At one instant the total acceleration vector rad tan at the other end makes a 60 degree angle with respect to the rod is 15 m s Angular velocity 2 rad s R 2 o v r 2 ar r and at r r r o 15cos 60 4r o r 1 88 m Chapter 11 Angular Momentum Torque T rF mar mr2 Nm o Increases if force applied from greater distance so best to hold wrench farther Newton s Second Law of Rotational Motion L I t 0 counterclockwise angular acceleration 0 clockwise angular acceleration W P Right hand rule curl fingers in direction of rotation thumb points in direction of Thumb points in direction of torque Angular Momentum L I o I of an object decreases then of object increases Example if a speed skater beings her arms in inertia decreases so she moves faster Example A car is moving with an initial velocity of 27 m s Each wheel has a r 0 3 m I 0 85 kgm 2 Total mass of the car 1200 kg o Transitional KE 1 1 2 2 5 KE m v 1200 27 4 37 10 J 2 2 o Rotational KE 2 2 1 1 v 1 27 2 3 KE I I 0 85 3 44 10 J 2 2 r 2 0 3 1 wheel 4 wheels 4 3 44 103 1 38 104 J o Total KE 5 4 5 4 37 10 J 1 38 10 J 4 51 10 J Chapter 13 Oscillations Periodic motion a motion that repeats again and again Frequency of oscillations per unit of time x Acos t v A sin t 2 a A cos t 1 2 2 PE K A co s t 2 1 KE m A 2 si n2 t 2 For a spring T 2 m and total energy kA 2 k I Pendulum T 2 mgl Smaller I rotates quickly smaller period Example For an object in Simple Harmonic Motion A 0 5 m f 2 Hz and t 0 05 s o 2 f 2 2 4 rad s o t 4 0 05 0 628 rad o Displacement x Acos t 0 5 cos 0 628 0 405 m o Velocity v A sin t 0 5 sin 0 628 3 69 m s o Acceleration at t 0 05 s a A 2 cos t 0 5 4 2 cos 0 628 63 9 m s 2