1, The left end of a rod of length d and rotational inertia | is attached to a frictionless horizontal surface by a frictionless pd pivat, as shown. Point C marks the center (midpoint) of the > L5y rod. The rod is initially motionless but is free to rolate arcund v e ] the pivol, A student will slide a disk of mass masx toward the rod with velocity v. perpendicular to the rod, and the disk will ' Yo stick to the rod a distance x from the pivot, The student O Disk wants the rod-disk system to end up with as much angular b ; a4 speed as possible, : a) Suppose the rod is much more massive than the disk, To Top View give the rod as much angular speed as possible, should the student make the disk hit the rod to the left of point C, at point C, or to the right of point C? To the left of C AtC To the right of C Briefly explain your reasoning without manipulating equations., b) On the Intermet, a student finds the following equation for the postcollision angular speed w of the My XV, rod in this situation: @ = . Regardless of whether this equation for angular speed is correct, does it agree with your qualitative reasoning in part (a)? In other words, does this equation for w have the expected dependence as reasoned in part (a)? Yes No Briefly explain your reasoning without deriving an equation for w. } Another student deriving an equation for the post collision angular speed w of the rod makes a T mistake and comes up with @@= . Without deriving the correct equation, how can you tell that '".r.'}k this equation is not plausible in other words, that it does not make physical sense? Briefly explain your reasoning. For parts (d} and (g}, do NOT assume that the rod is much more massive than the disk. d) Immediately before colliding with the rod, the disk's rotational inertia about the pivol is mlmxj and its angular momentum with respect to the pivotis m, v x. Derive an equation for the posteollision angular speed @ of the rod, Express your answer interms of d , my,,, I, x, v,, and physical constants, as appropriate. @) Consider the collision for which your equation in part (d) was derived, except now suppose the disk bounces backward off the rod instead of sticking to the rod. IS the posteollision angular speed of the rod when the disk bouncas off it greater than, less than, or equal to the postcollision angular speed of the rad when the disk sticks fo it? Greater than Less than Equal to Briefly explain your reasoning