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    A2讲义习题 (46) -Equilibrium of a rigid body under coplanar forces

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    A2讲义习题 (46) -Equilibrium of a rigid body under coplanar forces

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    A2讲义习题(46)-Equilibrium of a rigid body under coplanar forces(3)

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    A2讲义习题 (46) -Equilibrium of a rigid body under coplanar forces

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    yanghaoyi1985

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    © All Rights Reserved
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    A2 讲义习题(46)-Equilibrium of a rigid body under coplanar forces (3)

    1. When you mend a bicycle, you can turn it upside down so that it rests on the saddle and the
    handlebars. Suppose that you then spin the front wheel round so that it rotates with angular
    speed 10 rad s-1. If the rim has mass 1.6kg and radius 0.35 meters, how much kinetic energy
    does it have? Find the moment of inertia for the rim of the bicycle wheel, and use this to
    calculate the kinetic energy when the wheel rotates at 10 rad s-1.
    2. A cheer-leader spins a twirling stick, which consists of a rod 60cm long with a small metal
    ball attached at each end. The mass of each ball is 200grams. As a modeling simplification the
    balls can be treated as point masses, and the mass of the rod may be neglected.
    (a) find the moment of inertia of the twirling stick about its mid-point
    (b) find the kinetic energy of the stick if it makes 2 revolutions per second about its mid-point
    3. A light square lamina ABCD, whose mass can be neglected, has diagonals of length 1m.
    Particles of mass 1kg, 2kg, 3kg, 2kg are attached to the lamina at A, B, C and D respectively.

    A small hole is drilled in the lamina at a point 0 on AC such that AO=

    (a) Find the moment of inertia of the weighted lamina about 0.


    (b) The lamina is fastened to a wall by a nail at O, so that it can rotate freely about O in a vertical
    plane. Initially the lamina is held with C vertically above O, as shown in picture, and then
    released. If it is slightly disturbed from this position of unstable equilibrium, find its angular
    speed in the position when C is vertically below O
    4. The wheel of a cart is modeled as a set of 10 rods (the spokes), each of mass 4kg and length
    0.75m, and a rim of mass 24kg and radius 0.75m. Find the moment of inertia about the axle.
    5. Find the moment of inertia of a uniform rod of mass M and length 2l about a perpendicular
    axis through its center
    6. A uniform solid sphere of radius 0.8m and mass 100kg can rotate without friction about a
    horizontal axis through its center. A particle of mass 9kg is attached at the top of the sphere,
    where it rests in unstable equilibrium. When the sphere is slightly disturbed, equilibrium is
    broken and the particle descends. Find the angular speed of the sphere when it has rotated
    through half a revolution, so that the particle is at the lowest point.
    7. The bicycle wheel in question (1) comes to rest after it has turned through 30 revolutions.
    Assuming that the frictional couple slowing it down is constant, calculate its moment.
    8. A revolving door has moment of inertia 25 kg m 2 about its vertical central axis. A woman
    passing through the door exerts a horizontal force on one of the panels while it turns through
    an angle of 60°, so that the angular speed of the door reaches 1.8 rad s-1. The
    force is exerted at a distance 0.8m from the axis at right angles to the panel. She then reduces
    the force, so that the door goes on rotating at this speed until she has passed through it. After
    that the door goes on rotating through a further two revolutions before friction brings it to rest,
    find (a) the frictional couple opposing the rotation (assumed constant)
    (b) the force the woman exerts to start with
    (c) the force she exerts once the door has got up speed.

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