Physics 101: Lecture 13, Pg 1 Physics 101: Lecture 13 Rotational Kinetic Energy and Inertia Exam II

Physics 101: Lecture 13, Pg 2 Rotational Inertia, I l Tells how difficult it is get object spinning. Just like mass tells you how difficult it is to get object moving. è F net = m a Linear Motion è τ net = I α Rotational Motion I =  m i r i 2 (units kg m 2 ) l Note! Rotational Inertia depends on what you are spinning about (basically the r i in the equation). 13

Physics 101: Lecture 13, Pg 3 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 =  m r 2 Further mass is from axis of rotation, greater moment of inertia (harder to spin) 21

Physics 101: Lecture 13, Pg 4 Example: baseball bat

Physics 101: Lecture 13, Pg 5 Rotational Inertia Table For objects with finite number of masses, use I =  m r 2. For “continuous” objects, use table below. 33

Physics 101: Lecture 13, Pg 6 Example: Rolling An hoop with mass M, radius R, and moment of inertia I = MR 2 rolls without slipping down a plane inclined at an angle  = 30 o with respect to horizontal. What is its acceleration? l Consider CM motion and rotation about the CM separately when solving this problem  R I M 29

Physics 101: Lecture 13, Pg 7Rolling... l Static friction f causes rolling. It is an unknown, so we must solve for it. l First consider the free body diagram of the object and use l In the x direction l Now consider rotation about the CM and use  = I  R M  f y x 33 Mg 

Physics 101: Lecture 13, Pg 8 Rolling... l We have two equations: l We can combine these to eliminate f:  A R I M 36

Physics 101: Lecture 13, Pg 9 Rotational Energy l It is moving so it is a type of Kinetic Energy (go back and rename the first) Translational KE Rotaional KE

Physics 101: Lecture 13, Pg 10 Example: cylinder rolling l 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. H 43 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.

Physics 101: Lecture 13, Pg 11 Example: cylinder rolling l 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. H useand 43 Translational: Rotational: Ratio:

Physics 101: Lecture 13, Pg 12 Example: cylinder rolling l What is the velocity of the cylinder at the bottom of the ramp? H 45