Five objects of equal mass are shown below together with the axis about which th

Question

Five objects of equal mass are shown below together with the axis about which they are rotating. Select from the pull-down menus the objects in order of increasing rotational energy, with 1 having the smallest rotational energy and 5 having the highest rotational energy.

a) Solid Cylinder, about cylinder axis with R = 3 m and gw = 4 rad/s

b) Thin Spherical shell, about any diameter, with R = 3 m and gw = 4 rad/s

c) Thin rod, about axis through center, perpendicular to the length with l = 9 m and gw = 4 rad/s

d) Thin cylindrical shell, about cylinder axis with R = 2 m and gw = 5 rad/s

e) Solid Sphere, about any diameter, with R = 4 m and gw = 4 rad/s

Five objects of equal mass are shown below together with the axis about which they are rotating. Select from the pull-down menus the objects in order of increasing rotational energy, with 1 having the smallest rotational energy and 5 having the highest rotational energy. a) Solid Cylinder, about cylinder axis with R = 3 m and ?gw = 4 rad/s b) Thin Spherical shell, about any diameter, with R = 3 m and ?gw = 4 rad/s c) Thin rod, about axis through center, perpendicular to the length with l = 9 m and ?gw = 4 rad/s d) Thin cylindrical shell, about cylinder axis with R = 2 m and ?gw = 5 rad/s e) Solid Sphere, about any diameter, with R = 4 m and ?gw = 4 rad/s

Explanation / Answer

a) For solid cylinder        RK   = 0.5 I 2                 = 0.5 (0.5 M R2) 2                 = 0.25 M R2 2                 = 0.25 x M x 9 x 16                 = 36 M b) For solid cylinder        RK   = 0.5 I 2                 = 0.5 (0.666 M R2) 2                 = 0.333 M R2 2                 = 0.333 x M x 9 x 16                 = 48 M c) For thin rod I = ML2 / 12 = M x 81 / 12 = 6.75 M RK   = 0.5 I 2                 = 0.5 (ML2 / 12) 2                 = 0.5 (6.75M 2 )                 = 0.5x 6.75M x 16                 = 54 M d) I = 025 M R2       RK   = 0.5 I 2                 = 0.5 (0.25M R2) 2                 = 0.125 M R2 2                 = 0.125 x M x 4x 25                 = 12.5 M e) I = 2MR2 / 5    RK   = 0.5 I 2                 = 0.5 (0.4 M R2) 2                 = 0.2 M R2 2                 = 0.2x M x 16 x 16                 = 51.2 M Therefore             c >   e > b > a > d

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