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Physics 101: Lecture 13 Rotational Kinetic Energy and Inertia

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Physics 101: Lecture 13 Rotational Kinetic Energy and Inertia

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## Physics 101: Lecture 13 Rotational Kinetic Energy and Inertia

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**Exam II**Physics 101: Lecture 13Rotational Kinetic Energy and Inertia**Today’s Quizzes**1. A 2-kg stone is thrown vertically down with an initial velocity 12m/s from the tower of Pisa from a height of 30 m. Assume that the potential energy at the ground is zero. Neglect air resistance. • 1) What is the potential energy of the stone before falling (relative to the ground)? [5] • 2) What is the speed of the stone just before hitting the ground? • 2. A car does 45,000 J of work to travel at constant speed for 1.2 km along a horizontal road. • 1) What is the average retarding force acting on the car? • 2) The mass of the car is 1500 kg and the speed is 15 m/s. How much distance do you expect that the car can traverse after turning off its engine? • ------------------------------------------------------------------------------------------------------------------------ • 1. A 50 kg skier starts with an initial speed of 7m/s from the top of an incline. The incline has a slope of 20 degrees. Assume friction can be neglected. The total height of the hill is 120 m. • 1) What is the kinetic energy of the skier at the bottom of the incline? • 2)After reaching the bottom of the incline, the skier goes onto a horizontal surface with friction. If the coefficient of kinetic friction between the skier and the ground is 0.3, what is the distance she can traverse before she completely stops? • 2. John (his mass = 70 kg) and Mary (her mass = 55 kg) start at the same time from the top of two water-slides 10 m above the water level. John’s slide has an incline of 35 degrees while Mary’s slide has an incline of 15 degrees. Neglect friction. • What is John’s speed when he reaches the water? • What is Mary’s speed when she reaches the water? • Who gets to the water first? (Do not calculate!)**Yesterday I…**• A) Watched the parade • B) Watched fireworks • C) Prepared for Exam 2 • D) Both A and B • E) All of the above**Center of Mass = Balance point**Center of Mass Some objects can’t be balanced on a single point 46**Example: center of mass**1m m = 0.140 kg 0.1m M = 0.515**Summary**• Collisions and Explosions • Draw “before”, “after” • Define system so that Fext = 0 • Set up axes • Compute Ptotal “before” • Compute Ptotal “after” • Set them equal to each other • Center of Mass (Balance Point) 50**Rotational Inertia, I**• Tells how difficult it is get object spinning. Just like mass tells you how difficult it is to get object moving. • Fnet= m aLinear Motion • τnet = IαRotational Motion • I =S miri2 (units kg m2) • Note! Rotational Inertia depends on what you are spinning about (basically the ri in the equation). 13**Inertia Rods**Two batons have equal mass and length. Which will be “easier” to spin A) Mass on ends B) Same C) Mass in center I = S m r2 Further mass is from axis of rotation, greater moment of inertia (harder to spin) 21**Rotational Inertia Table**• For objects with finite number of masses, use I = S m r2. For “continuous” objects, use table below. 33**Example: Rolling**• An hoop with mass M, radius R, and moment of inertia I = MR2rolls without slipping down a plane inclined at an angle = 30o with respect to horizontal. What is its acceleration? • Consider CM motion and rotation about the CM separately when solving this problem I M R 29**y**f x Mg Rolling... • Static friction f causes rolling. It is an unknown, so we must solve for it. • First consider the free body diagram of the object and use • In the x direction • Now consider rotation about the CMand use =I M R 33**Rolling...**• We have two equations: • We can combine these to eliminate f: I A M R 36**What will change the acceleration of an object rolling down**an incline plane? A. The mass of the object B. The radius of the object C. The type of object (solid, hollow, sphere, disk) D. The angle of the incline. E. C and D only**Rotational Energy**• It is moving so it is a type of Kinetic Energy (go back and rename the first) Rotaional KE Translational KE**H**Example: cylinder rolling • Consider a cylinder with radius R and mass M, rolling w/o slipping down a ramp. Determine the ratio of the translational to rotational KE. • Friction causes object to roll, but if it rolls w/o slipping friction does NO work! • W = F d cos q d is zero for point in contact • No dissipated work, energy is conserved • Need to include both translation and rotation kinetic energy. 43**use**and Example: cylinder rolling • Consider a cylinder with radius R and mass M, rolling w/o slipping down a ramp. Determine the ratio of the translational to rotational KE. Translational: Rotational: Ratio: H 43**Example: cylinder rolling**• What is the velocity of the cylinder at the bottom of the ramp? H 45