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I am not sure if implicit differentiation is the correct approach to this problem or not.
I am not sure if implicit differentiation is the correct approach to this problem or not. " "
A uniform sphere growing .7cm/min with a mass density of 5g/cm^3.If I(R)=moment of Inerta when radius=R, what are dI/dR and dI/dt at
Since the object is a sphere I start out with the equation for moment of Inertia being I=.4mR^2, m being the mass of the object and R being the radius. since R is radius the dr or change in radius will be .7cm/min. Too find the mass of the object I will multiply 5g/cm^3 * R^3 to cancel out the cm leaving only grams therefore the mass. Since m=5g/cm^3 * R^3 I will replace m in the equation with 5g/cm^3 * R^3.
The new equation is now I=.4(5g/cm^3*R^3)(R^2). The next step is where I am somewhat unsure. If I understand correctly I will need to use implicit differentiation to find the dI/dR and the dI/dt. This is fine except for the fact that i do not know where my dt will come from. When I differentiate the equation I come up with dI=10*R^4*dR.
You're on the right track, just missing one step.
dI/dR = 10 g / cm^3 * R^4, the same thing as your equation dI=10*R^4*dR.
By the chain rule dI/dt = dI/dR * dR/dt. = 10 g / cm^3 * R^4 * dR/dt.
Or alternatively your equation dI=10*R^4*dR gives you dI/dt = 10 R^4 * dR/dt directly.
After looking at the equations some more I think that I can set dt=R/(.7cm/min) to find my dt after that I do not know where to go.
You are very close here. However the given information is that dR/dt = .7 cm / min. Just use this with one of the forms given above.