Consider a cylindrical shell of constant density p, inner radius 7₁, outer radius R, and height H. Assume that the cylinder is oriented along the z-axis. (a) Find the mass, m, of the cylinder. (b) Show that the z-axis goes through the centre of mass of the cylinder
Consider a cylindrical shell of constant density p, inner radius 7₁, outer radius R, and height H. Assume that the cylinder is oriented along the z-axis. (a) Find the mass, m, of the cylinder. (b) Show that the z-axis goes through the centre of mass of the cylinder
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Transcribed Image Text:Consider a cylindrical shell of constant density p, inner radius r₁, outer radius R, and height
H. Assume that the cylinder is oriented along the z-axis.
(a) Find the mass, m, of the cylinder.
(b) Show that the z-axis goes through the centre of mass of the cylinder
Transcribed Image Text:The moment of inertia for a set of objects of mass m; rotating about a common axis is
defined as
1 = Σm₁r?
2
where r, is the distance of the ith object to the axis of rotation. If there are many particles
that make up a larger object then this sum transforms into an integral,
4-fff or a.
I =
dV,
V
where p is the mass density and V the volume of the object.
In this exercise we will explore moment of inertia by rolling two objects down an incline
plane in the Experimental Math Lab Space.
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