Rotational Motion-solutions

Rotational Motion-solutions - le (txl65) Rotational Motion...

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Unformatted text preview: le (txl65) Rotational Motion mohanty (81440) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A cord is wrapped around a ywheel of inertia I = 1 2 mR 2 and radius R . A mass m is suspended by the cord. The system is released from rest and the suspended mass falls. R I m T g What is the acceleration of the suspended mass m ? 1. a = 2 3 g correct 2. a = 1 4 g 3. a = 3 2 g 4. a = g 5. a = 1 2 g 6. a = 2 g Explanation: Let the tension in the cord be T . For the mass, we have mg- T = ma . For the ywheel, we have T R = I = 1 2 mR 2 a R . From the second equation, we have T = 1 2 ma . Put it into the first equation and get mg- T = ma mg- 1 2 ma = ma mg = 3 2 ma , so a = mg 3 2 m = 2 3 g . 002 (part 1 of 2) 10.0 points Consider a spool with inner radius b and outer radius c . A string wraps around the inner stem in a counterclockwise manner. Starting from rest, the spool rolls when the string is pulled horizontally along AB as shown below. The force F is applied in such way that there is no slippage. F B A b c Determine the direction of rotation of the spool. 1. counterclockwise 2. clockwise correct 3. Cannot be determined Explanation: F net = ma , and (1) net = I = I a r , (2) Under the action of force F , the spool tends to accelerate linearly to the right, and to ro- tate counterclockwise. Therefore the contact point (presently at P , see the picture below), will have a tendency to move to the right against the surface. In turn, the friction force must point to the left. le (txl65) Rotational Motion mohanty (81440) 2 F B A b c f P Choose either A or P as the pivoting point. Choose A : the torque about A is = f ( c- b ) clockwise and the spool will rotate clockwise. Choose P : the torque about P is = F ( c- b ) clockwise and spool will still rotate clockwise. The agreement in the direction between these two different points of view actually tells us that our choice of the direction of f is correct. 003 (part 2 of 2) 10.0 points Choose the correct set of equations that gov- ern the motion of the spool. Here f is the magnitude of the frictional force between the spool and the horizontal surface, a is the lin- ear acceleration of the center of mass, and I is the moment of inertia about the center of mass of the spool. The torque will be evalu- ated with respect to the center of the spool. Be careful about the relative signs. 1. summationdisplay F x : F + f = ma summationdisplay : f c- F b = I a 2. summationdisplay F x : F- f = ma summationdisplay : f c- F b = I a 3. summationdisplay F x : F- f = ma summationdisplay : f c- F b = I a b 4....
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This note was uploaded on 04/05/2011 for the course SD ds taught by Professor Sdsd during the Spring '11 term at Tarrant County.

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Rotational Motion-solutions - le (txl65) Rotational Motion...

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