Question

An object with moment of inertia ?1 = 9.7 ? 10−4 ?? ∙ ?2 rotates at a speed of 3.0 ???/?. A 20 ? mass with moment of inertia ?2 = 1.32 ? 10−6 ?? ∙ ?2 is dropped onto the rotating object at a distance of 5.0 ?? from the center of mass. What is the angular velocity of the combined object and mass after the drop?

Answer #1

Using Angular momentum conservation:

Li = Lf

Li = Angular momentum of system initially = I1*w1

I1 = Moment of inertia of object = 9.7*10^-4

w1 = Initial angular velocity of system = 3.0 rev/s

Lf = Angular momentum of system finally = I1 + I2 + m*r^2

I2 = Moment of inertia of mass = 1.32*10^-6

m = mass = 20 g = 0.020 kg

r = distance of mass from center of mass of odd shaped = 5.0 cm = 0.05 m

w2 = final Angular velocity of system = ?? rev/s

So,

I1*w1 = (I1 + I2 + m*r^2)*w2

9.7*10^-4*3 = (9.7*10^-4 + 1.32*10^-6 + 0.020*0.05^2)*w2

w2 = (3*9.7*10^-4)/(9.7*10^-4 + 1.32*10^-6 + 0.020*0.05^2)

**w2 = 2.85 rev/sec =** angular velocity of the
combined object and mass after the drop

An object with moment of inertia ?1 = 9.7 ? 10−4 ?? ∙ ?2 rotates
at a speed of 3.0 ???/?. A 20 ? mass with moment of inertia ?2 =
1.32 ? 10−6 ?? ∙ ?2 is dropped onto the rotating object at a
distance of 5.0 ?? from the center of mass. What is the angular
velocity of the combined object and mass after the drop?
Please don't forget to state the combined mass after the
drop!!!

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