Given a falling mass m to apply a constant net torque to a \"dumbbell-shaped\" s

Question

Given a falling mass m to apply a constant net torque to a "dumbbell-shaped" system of masses M attached to a rotatable post. We will measure the change in velocity of a flag at the end of the dumbbell as the mass descends and from this measurement deduce the angular acceleration produced by the torque. Using the knowledge of physics we can determine the moment of inertia of the dumbbell.

Here are some relationships: v=R; =R; =I; =rFsin()=rF; T=mg(g-)=F

a) We can use the relationship between torque and angular acceleration as shown by these equations;

=(Inertia)(acceleration) or =Ia and a=ar=a(r/R) ; to solve for the moment of inertia in terms of quantities we can measure :

I=mr^2(gR/r-1)

Explanation / Answer

we know that . F=mg(g-a) (equation of motion of the mass) F*R/I=a/R. (of the dumbbell) so that mg*R^2(g-a)/I=a. so that I=mg*R^2(g/a-1) where a=a'*R. so that we have. I=mg*R^2(gR/a'R-1) -------- moment of inertia at the center because dm*r^2 alway smaller than dm*R^2 where R be radius of the dumbbell. so that I

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