homework and exercises - Calculating moment of inertia for a cylinder . . . However, the moment of inertia I looked up in a physics textbook is exactly two times this (the factor is $1 2,$ not $1 4$) I also solved for the moment of inertia of a sphere and similarly got exactly half of the accepted answer
Polar moment of inertia of a cylinder - Physics Stack Exchange 1 So I know the polar moment of inertia of a solid cylinder is: $$ I= \frac {1} {2} mr^2 $$ My question arises with the polar moment of inertia uses for solid cylinders in my mechanics of materials book, which is: $$ J=\frac {\pi} {2}r^4 $$ Don't these describe the same thing? Or am I mistaken in this, or simply overlooking something?
Why would a hollow cylinder lose a race with a solid one? Since the value of the moment of inertia determines the final acceleration then it is related to it, by other means, yes, it is the smaller moment of inertia of the solid cylinder that made it accelerate faster than the hollow one Its smaller value made it possible that the final acceleration would be 2 3gsin0
Moment of inertia of a cylinder? - Physics Forums Homework Statement the moment of inertia of A cylinder of height 2h radius (a) and uniform mass density ρ about a line x=y=z using multiple integration Homework Equations I=ρ∫s^2*dV where the integral is over the volume V of cylinder and s is the perpendicular distance to the axis of
Why does moment of inertia stop at 1 2 as solidness of a cylinder . . . For example, the moment of inertia for a solid sphere with uniform density is $\frac25 mr^2 = 0 4 mr^2$ But if you care about the moment of inertia of the Earth, you have to account for the Earth's differentiation, where most of the dense iron sank out of the mantle into the core; the Earth's actual moment of inertia is closer to $0 33 mr^2$
Moment of Inertia of a cylinder with varying density A cylinder with radius R and mass M has density that increases linearly with distance r from the cylinder axis, ρ = αr, where α is a positive constant Calculate the moment of inertia of the cylinder about a longitudinal axis through its center in terms of M and R
Moment of Inertia Homework: Solving for Force P - Physics Forums Homework Statement A light, flexible rope is wrapped several times around a hollow cylinder with a weight of 55 0 N and a radius of 0 25 m, that rotates without friction about a fixed horizontal axis The cylinder is attached to the axle by spokes of a negligible moment of inertia The