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Kaplunovsky - exam 04

# Kaplunovsky - exam 04 - midterm 04 Due May 2 2007 11:00 pm...

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midterm 04 – – Due: May 2 2007, 11:00 pm 1 Question 1, chap -1, sect -1. part 1 of 1 7 points A 3 m long rod of negligible weight is at- tached on one end to a ball joint which allows the rod to rotate in all directions. The free end of the rod points 30 above the Eastward horizontal direction. A 50 N force directed vertically Down is applied at the rod’s free end. What is the direction of the torque due to this force (relative to the pivot end of the rod)? 1. Horizontally Southward 2. Down and Eastward 3. Vertically Up 4. Insufficient data to determine the direc- tion. 5. Horizontally Westward 6. Horizontally Eastward 7. The torque vanishes 8. Horizontally Northward correct 9. Vertically Down 10. Up and Southwest Explanation: Use the right hand rule for vector τ = vector X × vector F : Stick your right thumb parallel to the rod — diagonally upward of East — and let your fingers point in the direction of the force — vertically Down. Consequently, the plain of your hand is vertical and your palm faces horizontally Northward. Alternatively, you may use a right coordi- nate system: the x axis points East, the y axis point North and the z axis points Up. In terms of the unit vectors ˆ ı , ˆ and ˆ k , we have a force vector F = - F ˆ k acting at the location vector X = ( L cos θ ı - ( L sin θ ) ˆ k . Consequently, the torque vector τ = vector X × vector F = - FL cos θ ı × ˆ k ) + FL sin θ ( ˆ k × ˆ k ) = - FL cos θ ( - ˆ ) + FL sin θ (0) = +( FL cos θ ) ˆ points along the positive y axis – horizontally Northward. Question 2, chap 13, sect 3. part 1 of 1 7 points A figure skater on ice spins on one foot. She pulls in her arms and her angular speed increases. Physically, this happens because ... ? Choose the reason from the list below; if two or more reasons seem plausible, choose the most important reason. 1. Her angular speed increases because her potential energy increases as her arms come in. 2. Her angular speed increases because air friction is reduced as her arms come in. 3. Her angular speed is unrelated to her arms. She pulls them in at the same time as she speeds up her spin because it looks better this way. 4. Her angular speed increases because she is undergoing uniformly accelerated angular motion. 5. Her angular speed increases because by pulling in her arms she creates a net torque in the direction of rotation. 6. Her angular speed increases because her angular momentum remains the same but her moment of inertia decreases. correct 7. Her angular speed increases because her angular momentum increases. Explanation: When a skater spins on one foot — or rather on just the toe of one skate — the external

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midterm 04 – – Due: May 2 2007, 11:00 pm 2 forces acting on her produce no net torque because of zero lever arms. Consequently, the skater’s angular momentum is conserved, L = = const .
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Kaplunovsky - exam 04 - midterm 04 Due May 2 2007 11:00 pm...

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