in fig. 15-42, the pendu- lum consists of a uniform disk with radius r 10.0 cm and mass 500 g attached to a uniform rod with length l 500 mm and mass 270 g. (a) calculate the rotational

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The rotational of the pendulum was found to be 0.205kg⋅m2

define rotational ?

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"rotately reward all selected pupils"

The rotational inertia of a uniform disc rotated at its centre is 21Mr2, where M is its mass and r is its radius. The disc in this problem spins at a point offset from its centre by r+L, where L is the length of the rod, hence its rotational inertia is 21Mr2+21M(L+r)2 according to the parallel-axis theorem. The rod has a rotational inertia of mL2/3, where m is its mass. The disc and rod's total rotational inertia equals

I=21Mr2+M(L+r)2+31mL2

  =21(0.500kg)(0.100m)2+(0.500kg)(0.500m+0.100m)2+31(0.270kg)(0.500m)2

=0.205kg⋅m2

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