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Unformatted text preview: Solution for Long-answer Homework 22 Torque and rolling motion problems Solution to Long-answer Homework Problem 22.1() Problem: Consider an object undergoing uniform circular motion, at constant speed v and radius r . In the following questions, carefully does not mean the answer has to be long and wordy, it just means you need to make sure you demonstrate an understanding of the important concept or fundamental law that supports your answer. (a)What is the magnitude of its acceleration? (b)Carefully explain why it has an acceleration, and if there is a torque on the object. (c)Draw a diagram showing the path of the object, and the direction it is travelling at some point on the path. For that point, draw the acceleration vector for the object and label it (c). (d)Now assume the object is still going in the same circle of radius r , but its speed is increasing. Draw the acceleration vector for the same point in the path as before, but label this one (d). Be neat so we can clearly tell which is which. (e)For this case of increasing speed, if the speed is increasing uniformly, what is the angular quantity related to motion that stays the same? What angular quantity is changing that could be calculated from the constant quantity and time? Write the equation between the two quantities relating them to time. (f)For this case of increasing speed, is there a torque on the object? Carefully explain why. (g)Now, assume that the object is back to uniform circular motion. While it is circling, a puck with the same mass as the object is placed so that it will be struck by the rotating object. The collisiion is perfectly elastic, and the surface is frictionless. Draw a picture showing where the puck is placed, and what its path looks like after it is struck. (h)What are the two conserved quantities in this interaction? (i)For your quantities in part h, rewrite them so they are in terms of m o , the mass of the rotating object v i,o , the initial speed of the rotating object, the final velocity of the puck, v f , and v f,o , the final speed of the rotating object. No I s should be left. You do not need to solve these equations. Solution to Part (a) The magnitude of the acceleration is given by a c = v 2 r , Grading Key: Part (a) 1 Points 1 point(s) : found the right formula Solution to Part (b) Since the direction is constantly changing, even though the speed isnt. Grading Key: Part (b) 3 Points 1 point(s) : velocity direction is changing 2 point(s) : angular momentum is constant, or no angular acceleration, so no torque (1 pt if something reasonable, but didnt quite find the right words) Solution to Part (c) 1 The object is travelling in a circle, with acceleration perpendicular to velocity, directed towards the center of the motion. It is traveling in a direction tangent to the circular path....
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