Phys 201 1nd Edition Lecture 9 Outline of Last Lecture I. Friction coefficient and adding friction to measures of force.Outline of Current Lecture II. Circular MotionIII. EquationsA. Arc LengthB. Centripetal AccelerationC. Angular VelocityD. Period and FrequencyIV. Connecting EquationsV. Force with Circular MotionCurrent LectureCircular motion:Uniform circular motion refers to when an object is moving at a constant speed in a circle. However, when you move around a circle, the direction in which you are moving is constantly changing. This means that the velocity is always changing, which means that there is acceleration, even if the speed is constant.Arc Length:Distance between two points on the outside of a circle is referred to as the arc length, and is usually represented by the letter S. Arc length can be calculated with the length of the radius and the angle between the radii. Therefore, for a circle with a radius r, and an angle between radii θ, the arc length can be calculated as;S=rθ or ΔS=rΔθCentripetal Acceleration:When referring to acceleration of an object around a circle, we use the term centripetal acceleration, which is usually represented as ac. Centripetal means the center point, so we are literally talking about the acceleration around the point in the middle of the circle. The centripetal acceleration of an object moving around a circle with a radius r, at a speed of v, can be calculated as;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.ac=V2/rBy this equation, we can see that the size of the circle affects the acceleration of an object traveling around it. As the size of the circle gets smaller, the acceleration increases.Angular velocity:Angular velocity, which is represented by Ω, refers to the speed at which an objects position changes in reference to the center of the circle. Remember, the angle θ represents change in position. Therefore, you can measure angular velocity as;Ω=Δθ/ΔtPeriod and Frequency:The period, represented by Τ, represents the amount of time it takes to complete one full circle. Frequency, represented by f, represents the number of circles completed in one second, though the common measure for frequency is rpm(revolutions per minute). This means that frequency and period are inverses of one another. To represent this as an equation;f=revolutions/secondsT=1/fAll of the equations we use to describe a circle are connected. This means that given most any information about a circle, we can calculate frequency, period, angular velocity, arc length and centripetal acceleration. i.e. Ω= Δθ/Δt = V/r = 2πf = 2π/T = (ΔS/Δt)/rac = V2/r = (rΩ)2/r = rΩ2We can apply these equations and measures to what we know about forces to solve for problems involving circular motion. Fnet= mac = m(V2/r) = m(4π2r/T2)Example: A 900-kg car moving at 80 m/s takes a turn around a circle with a radius of 250.0 m. What is the net force acting on the car?Fnet =macac= V2/r = 802/250 = 25.6m/s2Fnet=(900)(25.6)=23040NAssume that this represents the maximum speed that this car can travel around this track without skidding off of the track. What is the friction coefficient acting on the car?Ffric=μnIn this case, n=mg=(900)(9.81)=8829NBecause this is the maximum speed the car can travel on this track, Ffric=Fnet =23040NFfric=Fnet =23040N = μn = μ(8829N)μ=2.61Alternately, because Ffric=Fnet , μmg=mac. This means that we can find the friction coefficient by dividing the centripetal acceleration by the acceleration of