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Grade: 11

                        

In this problem we seek to compute the rotational inertia of a disk of mass M and radius R about an axis through its center and perpendicular to its surface. Consider a mass element dm in the shape of a ring of radius r and width dr (see Fig). (a) What is the mass dill of this element, expressed as a fraction of the total mass M of the disk? (b) What is the rotational inertia dI of this element? (c) Integrate the result of part (b) to find the rotational inertia of the entire disk.

In this problem we seek to compute  the rotational  inertia of a disk of mass M and radius R about an axis through its center and perpendicular  to its surface. Consider a mass element dm in the shape of a ring of radius r and width dr (see Fig). (a) What is the mass dill of this element,  expressed  as a fraction of the total mass M of the disk? (b) What is the rotational inertia dI of this element? (c) Integrate the result of part (b) to find the rotational inertia of the entire disk.

5 years ago

Answers : (1)

Aditi Chauhan
askIITians Faculty
396 Points
							236-1180_1.PNG
236-306_1.PNG
236-2423_1.PNG
Therefore, the rotational inertia of the circular disc about the axis of rotation passing through the center and perpendicular to the plane of disk is236-2484_1.PNG
5 years ago
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