A thin uniform rod has a length of 0.500 m and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod has an angular velocity of 0.400 rad/s and a moment of inertia about the axis of 3.00 ×10?3 kg · m2. A bug initially standing on the rod at the axis of rotation decides to crawl out to the other end of the rod. When the bug has reached the end of the rod and sits there, its tangential speed is 0.160 m/s. The bug can be treated as a point mass. (a) What is the mass of the rod? (b) What is the mass of the bug?
Solution to 50E Step 1 Length of the rod=0.5m Angular velocity of the rod =0.4rad/s -3 2 Moment of inertia about the axis=3x10 kgm Tangential speed of the bug =0.16m/s Step 2 (a) 2 Moment of inertia for the rod=()ML -3 2 2 I=3x10 kgm =()ML -3 2 3x10 x3/(L) =M M=9 x10 /0.25 M=0.036Kg Mass of the rod =36kg