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Unformatted text preview: le (txl65) Rotational Motion mohanty (81440) 1 This printout should have 24 questions. Multiplechoice 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.
 Spring '11
 sdsd

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