1. Circular Motion: Problem Solving 8.01 W04D3

2. Today’s Reading Assignment: W04D3 Problem Solving Strategy: Circular Motion Dynamics

3. Concept Question: Tension and String Theory A ball is suspended from a vertical rod by two strings of equal strength and equal length. The strings are very light and do not stretch. The rod is spun with a constant angular acceleration. Which string breaks first? 1.the upper string 2.the lower string 3.they break simultaneously 4.cannot tell without more information

4. Group Problem: Tension and String Theory A ball of mass m is suspended from a vertical rod by two strings of equal strength and equal length l. The strings are very light and do not stretch. The rod is spun with a constant angular speed ω. What are the tensions in the two strings?

5. Group Problem: Tension in Strings Two objects of equal mass m are whirling around a shaft with a constant angular velocity ω. The first object is a distance d from the central axis, and the second object is a distance 2d from the axis. You may ignore the mass of the strings and neglect the effect of gravity. What are tensions in the string between the inner object and the outer object and the string between the shaft and the inner object?

6. Group Problem: Tension in a Spinning Rope a) Divide the rope into small pieces of length Δr. Consider the piece located a distance r from the shaft. Draw a free body force diagram on that small piece. b) Apply Newton’s Second Law to that small piece and find in the limit as Δr approaches zero, a differential equation relating dT/dr to the distance r from the shaft. c) Integrate the differential equation you found in part b) to find the tension in the rope as a function of distance from the shaft. A uniform rope of mass m and length L is attached to shaft that is rotating at constant angular velocity ω. You may ignore the effect of gravitation.

7. Next Reading Assignment: W05D1 Young and Freedman: 6.1-6.4 Review Module: Scalar Product