PHY 101 1nd Edition Lecture 18 Outline of Last Lecture I 6 2 Conservation of Momentum II More on Conservation of Momentum III 6 3 Collision in 1D IV Perfectly Inelastic in 1D Outline of Current Lecture V Elastic Collision in 1D VI 6 4 Glancing Collisions VII Problem Solving 2D Collisions VIII Chapter 7 Rotational Motion IX 7 1 Angular Speed and Angular Acceleration X Rigid Body XI Sign of Angular Displacement Speed Acceleration Current Lecture Elastic Collision in 1D Both momentum are conserved in an elastic collision Conservation of momentum m1v1f m2v2f m1v1i m2v2i o Notice sign of Velocity Conservation fo KE 1 2m1v1f2 1 2m2v2f2 1 2m1v1i2 1 2m2v2i2 For ID elastic collision it can be shown as o v1f v1i v2f v2i o The summation of object 1 s initial final velocity equals that of object 2 Ex Pool o 2 billiard balls of identical mass m Ball 1 moves with a velocity v toward ball 2 Ball 2 is initially at rest Assume the collision is elastic What is the velocity of each ball after the collision o Rearrange M v1f v1i mv2f v1f v1i v2f o on the other hand for elastic collision v1f v1i v2f v2i o add both sides of the above equations 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 v1f v1i v1f v1i 0 V1f 0 the first ball stops o From eq 2 v1f v1i v2f v2f v1i o After the collision the velocity of the 2nd ball equals the initial velocity of the 1st ball Velocities are switched after collision 6 4 Glancing Collisions Collision in 2D Conservation of momentum o Pxi Pxf x component o Pyi Pyf y component Explicit form o M1v1xi m2v2xi m1v1xf m2v2xf o M1v1yi m2v2yi m1v1yf m2v2yf Example Before collision m1 has horizontal velocity v1i m2 is at rest After collision m1 has final velocity v1f m2 has final v2f Components of momentum o Initial Pxi m1v1 to m1v1i Pyi 0 o Final Pxf m1v1fcos m2v2fcos Pyf m1v1fsin m2v2sin o Initial final If the collision is elastic we also have conservation of energy o 1 2m1v1i2 1 2m1v1f2 1 2m2v2f2 For perfectly inelastic collision both objects have the same final velocity Problem solving 2D collisions Sketch a diagram coordinates x y axes Conservation of momentum If the collision is elastic conservation of KE If the collision is perfectly inelastic v1f v2f Solve for the equations of unknown variables Chapter 7 Rotational Motion 7 1 Angular Speed Angular Acceleration Linear motion position x changes with respect to time Rotational motion angle changes with respect to time o Angular displacement o f i o Unit radian 1 rad 360 2 57 3 o Angle in radian is defined as the arc length s along a circle divided by the radius r s r How do we measure how fast a wheel spins rotates o Angular speed omega o t unit rad s How about the rate of change of the angular speed o Angular acceleration alpha o f i tf ti t unit rad s2 Rigid Body every point on the object undergoes the same circular motion about a rotation axis O all points in a rigid body have o same angular displacement f i o same angular speed o same angular acceleration Sign of Angular Displacement Speed and Acceleration For a rigid body every point has the same angular displacement speed and acceleration Angular displacement speed and acceleration can be positive or negative Angular speed is defined as positive if is increasing i e the rotation is counterclockwise Speed is negative if is decreasing clockwise rotation Ex Revolution minute to radians second o The magnetic platter of a hard disk spins at an angular speed of 7200 rpm o A what is the angular speed in rad s o Solution 1 revolution 2 radian 7200 rpm 7200 x 2 rad 60 s 754 rad s