![]() B A Four kids (mass m) are riding on a (light) merry-go-round rotating with angular velocity w=3 rad/s. 263 of book).Physics 101: Lecture 13, Pg 11 Merry Go Round KE = 4 x ½ m v2 = 4 x ½ m w r2 = ½ I w2 Where I = 4 m r2 Further mass is from axis of rotation, greater KE it has. For “continuous” objects, use table below (p. Ktran = ½ m v2 Linear Motion Krot = ½ I w2 Rotational Motion I = S miri2 (units kg m2) Note! Rotational Inertia (or “Moment of Inertia”) depends on what you are spinning about (basically the ri in the equation).Physics 101: Lecture 13, Pg 10 Rotational Inertia Table For objects with finite number of masses, use I = S m r2. Just like mass tells you how much “work” is required to get object moving. MPhysics 101: Lecture 13, Pg 9 Rotational Inertia I Tells how much “work” is required to get object spinning. At bottom, bucket has zero velocity, energy must be in flywheel!Physics 101: Lecture 13, Pg 8 Rotational Kinetic Energy Consider a mass M on the end of a string being spun around in a circle with radius r and angular frequency w Mass has speed v = w r Mass has kinetic energy » K = ½ M v2 » = ½ M w2 r2 Rotational Kinetic Energy is energy due to circular motion of object. Where has this energy gone? A) Kinetic Energy of bucket B) Kinetic Energy of flywheel C) Both 1 and 2. z +wPhysics 101: Lecture 13, Pg 7 Energy ACT/demo When the bucket reaches the bottom, it’s potential energy has decreased by an amount mgh. Clockwise (decreasing q) is usually called negative. Counter-clockwise (increasing q) is usually called positive. This is usually called the “z” axis (we usually omit the z subscript for simplicity). what is positive and negative) Whenever we talk about rotation, it is implied that there is a rotation “axis”. ![]() ![]() ![]() Physics 101: Lecture 13, Pg 1 Physics 101: Lecture 13 Rotational Kinetic Energy and Rotational Inertia Exam IIPhysics 101: Lecture 13, Pg 2 F1-ATPase Rotary motor in biology #1Physics 101: Lecture 13, Pg 3 Rotary motor in biology #2 Bacterial flagellumPhysics 101: Lecture 13, Pg 4 Overview of Semester Newton’s Laws S F = m a Work-Energy S F = m a multiply both sides by d S W = DKE Energy is “conserved” Useful when know Work done by forces Impulse-Momentum S F = m a multiply both sides by Dt S I = Dp Momentum is “conserved” Useful when know about EXTERNAL forces Works in each direction independentlyPhysics 101: Lecture 13, Pg 5 Linear and Angular Motion Linear Angular Displacement x q Velocity v w Acceleration a a Inertia m I KE ½ m v2 N2L F=ma Momentum p = mv Today!Physics 101: Lecture 13, Pg 6 Comment on axes and sign (i.e. ![]()
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