The angular momentum of the spinning basketball is 0.6912 kg∙m 2/s. This can be easily determined by the application of the Parallel Axis Theorem since we can consider that the rectangle centroid is located at a distance equal to h/2 from the base. If the basketball weighs 0.6000 kg and has a radius of 0.1200 m, what is the angular momentum of the basketball?Īnswer:The angular momentum of the basketball can be found using the moment of inertia of a hollow sphere, and the formula. If we talk about an axis passing through the base, the moment of inertia of a rectangle is expressed as: I bh 3 / 3.
![moment of inertia of a circle with a hole moment of inertia of a circle with a hole](https://i.pinimg.com/originals/ce/2c/c0/ce2cc051d3696b183e2223338b81c7ee.jpg)
The moment of inertia of a hollow sphere is, where M is the mass and R is the radius. The angular momentum of this DVD disc is 0.00576 kg∙m 2/s.Ģ) A basketball spinning on an athlete's finger has angular velocity ω = 120.0 rad/s. What is the angular momentum of this disc?Īnswer: The angular momentum can be found using the formula, and the moment of inertia of a solid disc (ignoring the hole in the middle). When a DVD in a certain machine starts playing, it has an angular velocity of 160.0 radians/s. The moment of inertia of a solid disc is, where M is the mass of the disc, and R is the radius. Two point masses, m 1 and m 2, with reduced mass μ and separated by a distance x, about an axis passing through the center of mass of the system and perpendicular to the line joining the two particles.1) A DVD disc has a radius of 0.0600 m, and a mass of 0.0200 kg. Point mass M at a distance r from the axis of rotation.Ī point mass does not have a moment of inertia around its own axis, but using the parallel axis theorem a moment of inertia around a distant axis of rotation is achieved. Find the moment of inertia for rotation about an axis through the center of the drilled hole. Question: Moment of Inertia of a Disk with a Hole: A hole of radius r has been drilled in a circular, flat plate of radius R. The mass of the body (as shown with the hole cut in it) is M. Learn more about various High School Physics topics such as gravitation, electrostatics, e.t.c. The center of the hole is at a distance d from the center of the circle. Watch Advance Illustrations and Lessons Online on Physics. In general, the moment of inertia is a tensor, see below. Moment of Inertia of a Disk with a Hole: A hole of radius r has been drilled in a circular, flat plate of radius R. This article mainly considers symmetric mass distributions, with constant density throughout the object, and the axis of rotation is taken to be through the center of mass unless otherwise specified.įollowing are scalar moments of inertia. When calculating moments of inertia, it is useful to remember that it is an additive function and exploit the parallel axis and perpendicular axis theorems. In general, it may not be straightforward to symbolically express the moment of inertia of shapes with more complicated mass distributions and lacking symmetry. Typically this occurs when the mass density is constant, but in some cases the density can vary throughout the object as well. Since the thickness t is much smaller than the plate dimension, the mass and the elemental mass of the thin plate can be expressed in terms of.
![moment of inertia of a circle with a hole moment of inertia of a circle with a hole](https://d2vlcm61l7u1fs.cloudfront.net/media%2Fc3a%2Fc3a1612a-dec4-49a9-8cec-89a32f58e456%2FphpDlMMf1.png)
Both the thickness and the material density are constant over the area.
![moment of inertia of a circle with a hole moment of inertia of a circle with a hole](https://i.ytimg.com/vi/mnTC3SvQqXg/maxresdefault.jpg)
The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.įor simple objects with geometric symmetry, one can often determine the moment of inertia in an exact closed-form expression. Consider a thin plate of area A with uniform thickness t and homogenouse material density. It should not be confused with the second moment of area, which is used in beam calculations. Mass moments of inertia have units of dimension ML 2( × 2). Moment of inertia, denoted by I, measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analogue to mass (which determines an object's resistance to linear acceleration).