A 5.00 kg solid disk with radius R=1.00 m has three 4.00 kg point masses mounted

Question

A 5.00 kg solid disk with radius R=1.00 m has three 4.00 kg point masses mounted at its outer edge. The 4.00 kg masses can be moved inward by a special apparatus.

a) What is the rotational inertial of this object about its center?

b) A string wrapped around the edge is used to apply a constant force F=8.00 N for 5.00s , find the angular speed and the Kinetic energy that results.

c) While already spinning, the 4.00 kg masses are move to a radius of 20.0cm. Find the new angular speed and kinetic energy (during this time F=0.)

Explanation / Answer

disc inertial = 1/2 M R2 =1/2x5x1x1=2.5

rotail inertial of masses mounted at outer edge = 3mR2 =3x4x1x1=12

a) total inertia = 14.5

torque =fXr = 8x1 =8 N-m =0.816 kg -m

torue = I x angular acceleration

angular acc =8/14.5 =.0563

angular velocity = angular acc x t =.0563*5=.281 rad/sec

k.e =1/2 i wxw=1/2x14.5x.281x.281=.572 kgm/2/sec2

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