Q. 56

Expert-verifiedFound in: Page 333

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

Consider a solid cone of radius R, height H, and mass M. The volume of a cone is 1/3 πHR^{2}

a. What is the distance from the apex (the point) to the center of mass? b. What is the moment of inertia for rotation about the axis of the cone? Hint: The moment of inertia can be calculated as the sum of the moments of inertia of lots of small pieces.

a) Center of mass is at 3/4 H from vertex.

b) The moment of inertia is 3Mr^{2}/10

A solid cone of radius R, height H, and mass M.

The volume of a cone is 1/3 πHR^{2}

Lets consider a differential disc with radius r at a distance of x from the vertex as shown in figure below.

The mass of the differential disc is dm.

density of the disk is can be calculated as

From the figure we can find

Now we can find the value of dm

Substitute the value we get

Now find the center of mass

A solid cone of radius R, height H, and mass M. The volume of a cone is 1/3 πHR^{2}

Find the moment of inertia using dm from equation (2)

So moment of inertia is

Now integrate to find moment of inertia

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