Kolej Matrikulasi Labuan Laman Rasmi

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                     MATRICULATION DIVISION

                                TUTORIAL 7


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 6.5103 rpm. When the motor is
         turned off the blades come to rest in 3.0 s. Calculate the angular
         acceleration.                                            (Ans: 227 rad s2)
   (b)   A pulley of radius 8.0 cm is connected by a string to a rotating motor which
         is rotating at 7.0103 rad s1 and reduced to 2.0103 rad s1 in 5.0 s.
         (i) the tangential acceleration of the string,
         (ii) the time taken to stop the pulley.
                                                                 (Ans: 80 m s2; 2 s)


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 s1.                                 (Ans: 4.5 kg m2 s1)
   (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 s1. 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 2.5102 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 s1)

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
   s1 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 s1; 6.66 J)


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 s1)

                                             1.5 m

                                     FIGURE 2
9. (a)   A rotating merry-go-round makes one complete revolution in 4.0 s.
         (i) the linear speed of a child seated 1.20 m from the centre,
         (ii) her acceleration.
                                                         (Ans: 1.89 m s1; 2.98 m s2)
   (b)   A merry-go-round accelerates from rest to 3.0 rad s1 in 24 s. The merry-
         go-round is a uniform disc of radius 7.0 m and mass 3.1104 kg. Determine
         the nett torque required to accelerate it.             (Ans: 9.50104 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 s1; 11.1 rad s1)