MP49- Rotational Dynamics - MasteringPhysics: Assignment...

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Unformatted text preview: MasteringPhysics: Assignment Print View 4/28/08 3:03 PM [ Print View ] PHYS 2211 ABCDE Spring 08 MP49: Rotational Dynamics Due at 11:59pm on Thursday, April 10, 2008 View Grading Details Finding Torque A force of magnitude , making an angle with the x axis, is applied to a particle located at point A, at Cartesian and the four reference points (i.e., A, B, C, and D) all lie in the xy plane. Rotation coordinates (0, 0) in the figure. The vector axes A - D lie parallel to the z axis and pass through each respective reference point. The torque of a force acting on a particle having a position vector with respect to a reference point (thus and , points from the reference point to the point at which the force acts) is equal to the cross product of the torque is this problem of , , and/or , where is the angle between and ; the direction of . The magnitude of and . For is perpendicular to both ; negative torque about a reference point corresponds to clockwise rotation. You must express when entering your answers. in terms Part A What is the torque Hint A.1 due to force about the point A? When force is applied at the pivot point Hint not displayed Express the torque about point A at Cartesian coordinates (0, 0). ANSWER: = 0 Part B What is the torque due to force about the point B? (B is the point at Cartesian coordinates (0, ), located a distance from the origin along the y axis.) Hint B.1 Finding with respect to a reference point Hint not displayed Express the torque about point B in terms of ANSWER: = , , , , and/or other given coordinate data. Part C What is the torque axis? Hint C.1 Clockwise or counterclockwise? Hint not displayed Express the torque about point C in terms of ANSWER: = , , , , and/or other given coordinate data. about the point C, located at a position given by Cartesian coordinates ( , 0), a distance along the x http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1114171 Page 1 of 4 MasteringPhysics: Assignment Print View 4/28/08 3:03 PM Part D What is the torque about the point D, located at a distance , , , from the origin and making an angle with the x axis? Express the torque about point D in terms of ANSWER: = , and/or other given coordinate data. Note that the cross product can also be expressed as a third-order determinant which simplifies to when and lie in the xy plane. Pivoted Rod with Unequal Masses A thin rod of mass and length is allowed to pivot freely about its center, as shown in the diagram. A small sphere of mass is attached to the left end of the rod, and a small sphere of mass is attached to the right end. The spheres are small enough that they can be considered point particles. The gravitational force acts downward, with the magnitude of the gravitational acceleration equal to . Part A What is the moment of inertia Hint A.1 of this assembly about the axis through which it is pivoted? Sum the component moments of inertia Hint not displayed Part A.2 Moment of inertia due to particle of mass Part not displayed Part A.3 Moment of inertia due to particle of mass Part not displayed Part A.4 Moment of inertia of the rod Part not displayed Express the moment of inertia in terms of ANSWER: , , , and . Remember, the length of the rod is , not . = Part B Suppose the rod is held at rest horizontally and then released. (Throughout the remainder of this problem, your answer may include the symbol , the moment of inertia of the assembly, whether or not you have answered the first part correctly.) What is the angular acceleration Part B.1 of the rod immediately after it is released? Relating the angular acceleration to the net torque Part not displayed Part B.2 Torque due to the sphere of mass Part not displayed Part B.3 Torque due to the sphere of mass Part not displayed Hint B.4 Torque due to forces acting on the rod http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1114171 Page 2 of 4 MasteringPhysics: Assignment Print View 4/28/08 3:03 PM Hint not displayed Take the counterclockwise direction to be positive. Express , and . ANSWER: = in terms of some or all of the variables , , , , Pulling a String to Accelerate a Wheel A bicycle wheel is mounted on a fixed, frictionless axle, as shown . A massless string is wound around the wheel's rim, and a constant horizontal force of magnitude starts pulling the string from the top of the wheel starting at time rotating. Suppose that at some later time pulled through a distance , where the wheel's mass, and not slip on the wheel. when the wheel is not the string has been . The wheel has moment of inertia is is a dimensionless number less than 1, is its radius. Assume that the string does Part A Find , the angular acceleration of the wheel, which results from pulling the string to the left. Use the standard convention that counterclockwise angular accelerations are positive. Part A.1 Relate torque about the axle to force applied to the wheel Part not displayed Part A.2 Relate torque on wheel to angular acceleration Part not displayed Express the angular acceleration, ANSWER: = , in terms of , , , and (but not ). Part B The force pulling the string is constant; therefore the magnitude of the angular acceleration of the wheel is constant for this configuration. Find the magnitude of the angular velocity of the wheel when the string has been pulled a distance . Note that there are two ways to find an expression for Hint B.1 What the no-slip case means ; these expressions look very different but are equivalent. Hint not displayed Hint B.2 Review of translational motion with constant acceleration Hint not displayed Part B.3 When has the string been pulled a distance ? Part not displayed Part B.4 Relating translational acceleration and angular acceleration Part not displayed Express the angular velocity of the wheel in terms of the displacement , the magnitude of the applied force, and the moment of inertia of the wheel , if you've found such a solution. Otherwise, following the hints for this part of the wheel in terms of the displacement , the wheel's radius , and should lead you to express the angular velocity . ANSWER: = http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1114171 Page 3 of 4 MasteringPhysics: Assignment Print View 4/28/08 3:03 PM This solution can be obtained from the equations of rotational motion and the equations of motion with constant acceleration. An alternate approach is to calculate the work done over the displacement by the force and equate this work to the increase in rotational kinetic energy of rotation of the wheel Part C Find , the speed of the string after it has been pulled by Part C.1 Relating the speed of the string over a distance . to the angular velocity Part not displayed Express the speed of the string in terms of ANSWER: = , , , and ; do not include , , or in your answer. Note that this is the speed that an object of mass with constant magnitude . (which is less than ) would attain if pulled a distance by a force Summary 3 of 3 items complete (105.12% avg. score) 3.15 of 3 points http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1114171 Page 4 of 4 ...
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This note was uploaded on 05/08/2008 for the course PHYSICS 2211 taught by Professor Uzer during the Spring '08 term at Georgia Institute of Technology.

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