Transcript Document
Chapter 9 β Energy and Momentum in Rotational Motion Peter Anderson [email protected] Office: PHYS 221 Office Hours: T,W 11am to 12pm Review Problem A woman rolls a cylindrical drum by pushing a board across its top. The drum moves through the distance L/2, which is half the boardβs length. The drum rolls smoothly without sliding or bouncing, and the board does not slide over the drum. A) What length of board rolls over the top of the drum? B) How far does the woman walk? Brief Review π =π×πΉ =πΌπΌ πΏ =π×π =πΌπ Conservation of Angular Momentum ππππ‘ = 0 β ΞπΏ = 0 Or πΏπ = πΏπ Quiz 1 A rhinoceros beetle rides the rim of a small disk that rotates like a merry-go-round. If the beetle crawls toward the center of the disk, does the moment of inertia of the beetle-disk systemβ¦ A) Increase B) Decrease C) Remain the Same Quiz 2 A rhinoceros beetle rides the rim of a small disk that rotates like a merry-go-round. If the beetle crawls toward the center of the disk, does the Angular momentum of the beetle-disk systemβ¦ A) Increase B) Decrease C) Remain the Same Quiz 3 A rhinoceros beetle rides the rim of a small disk that rotates like a merry-go-round. If the beetle crawls toward the center of the disk, does the angular speed of the beetle-disk systemβ¦ A) Increase B) Decrease C) Remain the Same Sample Problem 1 In the overhead view of the figure, four thin, uniform rods, each of mass M and length d = 0.50m, are rigidly connected to a vertical axle to form a turnstile. The turnstile rotates clockwise about the axle, which is attached to a floor, with initial angular velocity ππ = β2.0rad/s. A mud ball of mass m = M/3 and initial speed π£π = 12m/s is thrown along the path shown and sticks to the end of one rod. What is the final angular velocity ππ of the ball-turnstile system? Sample Problem 2 A bola, which consists of three heavy balls connected to a common point by identical lengths of sturdy string, is readied for launch by holding one of the balls overhead and rotating the wrist, causing the other two balls to rotate in a horizontal circle about the hand. The bola is then released, and its configuration rapidly changes from that in the overhead view of fig1 to that of fig2. Thus the rotation is initially around axis 1 through the ball that was held. Then it is around axis 2 through the center of mass. Are (a) the angular momentum and (b) the angular speed around axis 2 greater than, less than, or the same as that around axis 1?