{"id":30,"date":"2016-05-04T15:29:42","date_gmt":"2016-05-04T15:29:42","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/?page_id=30"},"modified":"2020-09-30T12:10:25","modified_gmt":"2020-09-30T12:10:25","slug":"tutorial-7","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/tutorial-7\/","title":{"rendered":"Tutorial 7"},"content":{"rendered":"

Angular momentum and rotational kinetic energy<\/strong><\/p>\n

 <\/p>\n

    \n
  1. (a) State the law of conservation of angular momentum.<\/li>\n<\/ol>\n

    (b)\u00a0\u00a0 State the expression for the angular momentum of an object in terms of its moment of inertia.<\/p>\n

    (c)\u00a0\u00a0 State the equation for the rotational kinetic energy of a rigid object.<\/p>\n

     <\/p>\n

      \n
    1. A bicycle wheel has a moment of inertia of 0.25 kgm2<\/sup> about its hub.<\/li>\n<\/ol>\n

      Calculate the angular momentum of the wheel when rotating at 120 r.p.m.<\/p>\n

       <\/p>\n

        \n
      1. A model aeroplane is flying in a horizontal circle at the end of a light wire. The mass of the aeroplane is 2.0 kg.\u00a0 The radius of the circular path is 20 m.\u00a0 The aeroplane makes 40 revolutions in one minute.<\/li>\n<\/ol>\n

        (a)\u00a0\u00a0 Calculate the linear velocity of the aeroplane.<\/p>\n

        (b)\u00a0\u00a0 Find the angular momentum of the aeroplane about the centre of the circle.<\/p>\n

        (c)\u00a0\u00a0 The wire suddenly breaks.\u00a0 What is the new angular momentum of the aeroplane about the centre of the circle?<\/p>\n

         <\/p>\n

          \n
        1. A shaft has a moment of inertia of 20 kgm2<\/sup> about its central axis. The shaft is rotating at 10 rpm.\u00a0 This shaft is locked onto another shaft, which is initially stationary.\u00a0 The second shaft has a moment of inertia of 30 kgm2<\/sup>.<\/li>\n<\/ol>\n

          (a)\u00a0\u00a0 Find the angular momentum of the combination after the shafts are locked together.<\/p>\n

          (b)\u00a0\u00a0 What is the angular velocity of the combination after the shafts are locked together?<\/p>\n

           <\/p>\n

            \n
          1. Which of the following are vector quantities:<\/li>\n<\/ol>\n

            torque, moment of inertia, angular velocity, tangential force, angular acceleration, rotational kinetic energy, radius of a circular motion.<\/p>\n

             <\/p>\n

              \n
            1. Two children are playing on a roundabout of mass 250 kg. The roundabout can be considered to be a solid disc of diameter 3.0 m.\u00a0 (Idisc<\/sub> = \u00bd MR2<\/sup>)<\/li>\n<\/ol>\n

              One child of mass 40 kg stands on the rim of the roundabout. The other child of mass 60 kg is positioned half way between the rim and the centre.<\/p>\n

              (a)\u00a0Calculate the total moment of inertia of the roundabout and children.<\/p>\n

              (b)\u00a0Determine the rotational kinetic energy of this system when it is rotating at 35\u00a0rpm.<\/p>\n

               <\/p>\n

                \n
              1. A disc has a moment of inertia of 2.5 kgm2<\/sup>. The disc is rotating at 2.0 rads-1<\/sup>.<\/li>\n<\/ol>\n

                (a)\u00a0Calculate the kinetic energy of the disc.<\/p>\n

                (b)\u00a0How much energy needs to be supplied to increase its angular velocity to 15\u00a0rads-1<\/sup>?<\/p>\n

                 <\/p>\n

                  \n
                1. A solid cylinder and a hollow cylinder have the same mass and the same radius.<\/li>\n<\/ol>\n\n\n\n
                  (a)\u00a0\u00a0 Which one has the larger moment of inertia about the central axis as shown opposite? You must justify your answer.<\/p>\n

                  (b)\u00a0\u00a0 The cylinders do not have the same length.\u00a0 Does this affect your answer to part (a)?\u00a0 Again you must\u00a0justify your answer.<\/td>\n

                  		\"Capture\"<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                   <\/p>\n

                    \n
                  1. A cylinder of mass 3.0 kg rolls down a slope without slipping. The radius R of the cylinder is 50 mm and its moment of inertia is \u00bdMR2<\/sup>.\u00a0 The slope has a length of 0.30 m and is inclined at 40o<\/sup> to the horizontal.<\/li>\n<\/ol>\n

                    (a)\u00a0\u00a0 Calculate the loss in gravitational potential energy as the cylinder rolls from the top of the slope to the bottom of the slope.<\/p>\n

                    (b)\u00a0\u00a0 Find the speed with which the cylinder reaches the bottom of the slope.<\/p>\n

                     <\/p>\n

                      \n
                    1. A turntable is rotating freely at 40 rpm about a vertical axis. A small mass of 50\u00a0g falls vertically onto the turntable and lands at a distance of 80 mm from the central axis.\u00a0 The rotation of the turntable is reduced to 33 rpm. Find the moment of inertia of the turntable.<\/li>\n<\/ol>\n

                       <\/p>\n

                        \n
                      1. An LP of mass 180g and diameter 30 cm is dropped onto a rotating turntable. The turntable has a moment of inertia about its axis of rotation of 5.0 x 10-3<\/sup>\u00a0kgm2<\/sup>.\u00a0 The turntable was initially rotating at 3.5 rads-1<\/sup>. Determine the common angular velocity of the turntable and the LP.<\/li>\n<\/ol>\n

                         <\/p>\n

                          \n
                        1. A skater with her arms pulled in has a moment of inertia of 1.5 kgm2<\/sup> about a vertical axis through the centre of her body. With her arms outstretched the moment of inertia is increased to 10 kgm2<\/sup>. With her arms pulled in, the skater is spinning at 30 rads-1<\/sup>.\u00a0 The skater then extends her arms.<\/li>\n<\/ol>\n

                          (a)\u00a0\u00a0 Calculate her final angular speed.<\/p>\n

                          (b)\u00a0\u00a0 Find the change in kinetic energy.<\/p>\n

                          (c)\u00a0\u00a0 Explain why there is a change in kinetic energy.<\/p>\n

                           <\/p>\n

                            \n
                          1. A skater is spinning at 3.0 rads-1<\/sup> with her arms and one leg outstretched.<\/li>\n<\/ol>\n

                            The angular speed is increased to 25 rads-1<\/sup> when she draws her arms and leg in.<\/p>\n

                            (a)\u00a0\u00a0 Explain why this movement of her arms and leg affects the rotational speed.<\/p>\n

                            (b)\u00a0\u00a0 Her moment of inertia about her spin axis is 5.0 kgm2<\/sup> with her arms and leg outstretched.\u00a0 Calculate her moment of inertia when her arms and leg are drawn in.<\/p>\n

                             <\/p>\n

                              \n
                            1. A roundabout has a moment of inertia of 300 kgm2<\/sup> about its axis of rotation. Three children, each of mass 20 kg, stand 2.0 m from the centre of the stationary roundabout.\u00a0 They all start to run round the roundabout in the same direction until they reach a speed of 3.0 ms-1<\/sup> relative to the roundabout. Calculate the angular velocity of the roundabout.<\/li>\n<\/ol>\n

                               <\/p>\n

                                \n
                              1. A disc is rotating at 100 rpm in a horizontal plane about a vertical axis. A small piece of plasticene is dropped vertically onto the disc and sticks at a position 50\u00a0mm from the centre of the disc.\u00a0 The plasticene has a mass of 20 g.\u00a0 The disc is slowed to 75\u00a0<\/sup>rpm.\u00a0 Calculate the moment of inertia of the disc.<\/li>\n<\/ol>\n

                                 <\/p>\n

                                  \n
                                1. The radius of a spherical neutron star is 20 km. The star rotates at 1800 rpm.<\/li>\n<\/ol>\n

                                  (a)\u00a0\u00a0 Calculate the velocity of a point on the equator of the star.<\/p>\n

                                  (b)\u00a0\u00a0 The mass of the neutron star is the same as the mass of the sun. What is the density of the neutron star?<\/p>\n

                                  (c)\u00a0\u00a0\u00a0The radius of a neutron is about 10-15<\/sup> m.\u00a0 Estimate the average spacing of the neutrons in the neutron star.<\/p>\n","protected":false},"excerpt":{"rendered":"

                                  Angular momentum and rotational kinetic energy   (a) State the law of conservation of angular momentum. (b)\u00a0\u00a0 State the expression for the angular momentum of an object in terms of its moment of inertia. (c)\u00a0\u00a0 State the equation for the rotational kinetic energy of a rigid object.   A bicycle wheel has a moment of … Continue reading Tutorial 7<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":6460,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-30","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/30","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/users\/6460"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/comments?post=30"}],"version-history":[{"count":3,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/30\/revisions"}],"predecessor-version":[{"id":132,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/30\/revisions\/132"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/media?parent=30"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}