6 - The rotational inertia apparatus has a falling mass rotati post (radi M=1 kg

Question

6 - The rotational inertia apparatus has a falling mass rotati post (radi M=1 kg that falls from a distance h = 1m to the ground. The rotating post has a radius of rpost = 0.01 m and two masses “m” rotating at a distance “R” from the post. The falling mass M achieves a max velocity VM .5 m/sec (just before hitting the ground) which imparts a maximum angular velocity o)post-masses (where VM=(o)post+masses).(rpost) to the rotating post and masses. Given that g = 9.8 m/s2 Using conservation of energy of the apparatus, calculate the moment of inertia "I" for the rotating post and masses in scientific notation and with the correct units.

Explanation / Answer

using law of conservation of energy

mgh= 1/2 I w^2 + 1/2 mv^2

I= moment of inertia

now v= r w ...===> w= v/r

mgh= 1/2 I V^2/r^2 + 1/2 mv^2

1 (1)(9.8) = 1/2 I (0.5^2 /0.01^2) +1/2 (1)(0.5)^2

9.8= 1250 I +0.125

1250 I= 9.675

I= 9.675/1250 = 7.74x10^-3 kgm^2

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