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SF017 MATRICULATION DIVISION MINISTRY OF EDUCATION MALAYSIA TUTORIAL 7 TOPIC 7: ROTATION OF A RIGID BODY 1. A boy and a girl are riding on a merry-go-round which is rotating at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement? A The boy B The girl C Both have the same non-zero angular displacement. D Both have zero angular displacement. 2. Which of the following statements is CORRECT for a rigid body that is rotating. A Its centre of rotation is its centre of mass. B All points on the body are moving with the same angular velocity. C All points on the body are moving with the same linear velocity. D Its center of rotation is at rest, i.e., not moving. 3. A man standing on a freely rotating frictionless platform holding two weights with his arms extended horizontally. If he pulled the weights inward horizontally to his chest, then the A angular velocity increase B angular velocity decrease C angular momentum increase D angular momentum decrease 4. (a) The blades in a blender rotate at a rate of 6.5103 rpm. When the motor is turned off the blades come to rest in 3.0 s. Calculate the angular acceleration. (Ans: 227 rad s2) (b) A pulley of radius 8.0 cm is connected by a string to a rotating motor which is rotating at 7.0103 rad s1 and reduced to 2.0103 rad s1 in 5.0 s. Calculate (i) the tangential acceleration of the string, (ii) the time taken to stop the pulley. (Ans: 80 m s2; 2 s) 1 SF017 5. (a) A uniform solid sphere of radius 0.50 m and mass 15 kg rotates about the z axis through its centre. Calculate its angular momentum when the angular velocity is 3.0 rad s1. (Ans: 4.5 kg m2 s1) (b) A figure skater increases her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3.0 rev s1. Her initial moment of inertia was 4.6 kg m2. (i) Calculate her final moment of inertia. (ii) How does she physically accomplish this change? (Ans: 0.77 kg m2) 6. (a) Why is it more difficult to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? (b) A merry-go-round of radius 2.0 m has a moment of inertia 2.5102 kg m2 and is rotating at 10 rpm. A child of mass 25 kg jumps onto the edge of the merry-go-round. Calculate the new angular velocity of merry-go-round. (Ans: 0.75 rad s1) 7. An object P of mass 300 g is placed on a stationary smooth horizontal disc. A string tied to P passes through a small hole O at the centre of the disc as shown in FIGURE 1. P revolves about the centre with tangential linear speed of 5.0 m s1 in a circle of radius 50 cm. The string is then pulled downwards slowly until P travels in a circle of radius 30 cm. P O FIGURE 1 (a) Sketch the force acting on P as it travels in a circle. (b) Calculate the linear velocity of P in the new circle. (c) Calculate the total work done to reduce the size of the circle. (Ans: 8.33 m s1; 6.66 J) 2 SF017 8. A pulley of radius 20 cm has moment of inertia 0.040 kg m2 about the axis through its centre. Part of a light string wraps round the pulley while the free end is tied to an object of mass 2.0 kg. The object is suspended 1.5 m above the ground and is stationary as in FIGURE 2. If the object is released, calculate its velocity at that instant when it reaches the ground. (Ans: 4.43 m s1) 1.5 m FIGURE 2 9. (a) A rotating merry-go-round makes one complete revolution in 4.0 s. Calculate (i) the linear speed of a child seated 1.20 m from the centre, (ii) her acceleration. (Ans: 1.89 m s1; 2.98 m s2) (b) A merry-go-round accelerates from rest to 3.0 rad s1 in 24 s. The merry- go-round is a uniform disc of radius 7.0 m and mass 3.1104 kg. Determine the nett torque required to accelerate it. (Ans: 9.50104 N m) 10. A small object of mass 200 g is placed on top of one end of a uniform horizontal rod PQ as shown in FIGURE 3. The rod has length 100 cm and moment of inertia of 0.050 kg m2 about an axis which passes through the end P and is perpendicular to the rod. The coefficient of static friction between the object and rod is 0.50. object P Q 100 cm FIGURE 3 Calculate the angular velocity of the rod (a) at the moment when the object is just about to slide on the rod. (b) immediately after the object has dropped off the rod. (Ans: 2.22 rad s1; 11.1 rad s1) 3

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Kolej Matrikulasi Labuan, kolej matrikulasi, kolej matrikulasi labuan kml, KEMENTERIAN PELAJARAN MALAYSIA, Video Challenge, Federal Territory of Labuan, Kuala Lumpur, Labuan Matriculation College, Wilayah Persekutuan, Kolej Matrikulasi Perlis

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posted: | 3/23/2011 |

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