PHY 101 1nd Edition Lecture 18Outline of Last Lecture I. 6.2 Conservation of MomentumII. More on Conservation of MomentumIII. 6.3 Collision in 1DIV. Perfectly Inelastic in 1DOutline of Current Lecture V. Elastic Collision in 1DVI. 6.4 Glancing CollisionsVII. Problem Solving: 2D CollisionsVIII. Chapter 7: Rotational Motion IX. 7.1 Angular Speed and Angular AccelerationX. Rigid BodyXI. Sign of Angular Displacement, Speed & AccelerationCurrent LectureElastic Collision in 1D- Both momentum & are conserved in an elastic collision- Conservation of momentum: m1v1f + m2v2f = m1v1i + m2v2io 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. Poolo 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) = -v2fo on the other hand for elastic collision: (v1f + v1i) = (v2f + v2i)o add both sides of the above equationsThese 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 stopso From eq. 2 (v1f + v1i) = v2f  v2f = v1io After the collision, the velocity of the 2nd ball equals the initial velocity of the 1st ball Velocities are switched after collision6.4 Glancing Collisions- Collision in 2D- Conservation of momentumo ΣPxi = ΣPxf  x-componento ΣPyi = ΣPyf  y-component- Explicit form:o M1v1xi + m2v2xi = m1v1xf + m2v2xfo 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 momentumo Initial ΣPxi = m1v1 to = m1v1i ΣPyi = 0o Final ΣPxf = m1v1fcosΘ + m2v2fcosφ ΣPyf = m1v1fsinΘ – m2v2sinφo Initial = final- If the collision is elastic, we also have conservation of energyo 1/2m1v1i2 = 1/2m1v1f2 + 1/2m2v2f2- For perfectly inelastic collision, both objects have the same final velocityProblem 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 variablesChapter 7: Rotational Motion7.1 Angular Speed & Angular Acceleration- Linear motion: position x changes with respect to time- Rotational motion: angle Θ changes with respect to timeo Angular displacement:o ΔΘ = Θf – Θio Unit: radian 1 rad = 360°/2Π = 57.3°o Angle in radian is defined as the arc length (s) along a circle divided by the radius r Θ = s/r- How do we measure how fast a wheel spins (rotates)?o Angular speed (omega)o ω = ΔΘ/Δt (unit: rad/s)- How about the rate of change of the angular speed?o Angular acceleration (alpha)o α = ωf – ωi/ tf – ti = Δω/Δt (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: ΔΘ = Θf – Θio same angular speed: ωo same angular acceleration: αSign 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 Θ is increasing (i.e., the rotation is counterclockwise)- Speed is negative if Θ is decreasing (clockwise rotation)- Ex. Revolution/minute to radians/secondo 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 = 2Π radian ω = 7200 rpm = 7200 x 2Π rad/ 60 s = 754