Announcements 1. HW8 due March 17 (after spring break). 2. Week of March 16 and 18 (after spring break) Prof. Detweiler will give lectures Profs. Chan and Hirschfeld will not hold office hours during that week Last time: rotational motion angle angular velocity angular acceleration s r t t measured in rad “” in rad/s “” in rad/s2 Angular velocity is a vector magnitude Vt R Vt R directions of tangential velocity vt and angular frequency vt vt vt Right Hand Rule out of screen Example: horizontal circle (from HW!) A 0.5 kg ball that is tied to the end of a 1.5-m light cord is revolved in a horizontal plane, with the cord making a 30 deg angle with the vertical. a) Determine the ball’s speed b) Now the ball is revolved so that it’s speed is 4.0 m/s. What angle does the cord make with the vertical? Nonuniform circular motion • The tangential component of the acceleration at is due to changing speed • The centripetal component of the acceleration ac is due to changing direction • Total acceleration can be found from these components a a a 2 t 2 C ac at a Don’t confuse: at r 2 v 2 ac r r Vertical Circle • Look at the forces at the top of the circle • The minimum speed at the top of the circle can be found vtop gR …i.e., the minimum speed to just stay on the track 7.75 In a popular amusement park ride, a rotating cylinder of radius 3.00 m is set in rotation at an angular speed of 5.00 rad/s. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider’s clothing and the wall is needed to keep the rider from slipping? 7.27 An air puck of mass 0.25 kg is tied to a string and allowed to revolve in a circle of radius 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.0 kg is tied to it. The suspended mass remains in equilibrium while the puck on the tabletop revolves. (a) What is the tension in the string? (b) What is the horizontal force acting on the puck? (c) What is the speed of the puck?