Substituting into the equation for kinetic energy, we find K 1 2 m v t 2 1 2 m ( r) 2 1 2 ( m r 2) 2. 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. We can relate the angular velocity to the magnitude of the translational velocity using the relation v t r, where r is the distance of the particle from the axis of rotation and v t is its tangential speed. The moment of inertia of a hollow sphere is, where M is the mass and R is the radius. Find Moment of Inertia of a Solid Sphere Calculator at CalcTown. 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. Find the moment of inertia of a hollow sphere about a chord that is at a distance of 3 m from the centre of the sphere. 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). If we let denote the angle between the axis of rotation and the distance R R of each particle, then the lever arm of each particle is simply just r Rsin r R s i n. When a DVD in a certain machine starts playing, it has an angular velocity of 160.0 radians/s. Let’s explore What is Moment of Inertia of Sphere Solid & Hollow Let’s try to understand the moment of inertia of sphere basics. Let us calculate the moment of inertia of a hollow sphere having a mass of 55.0 kg and a radius of 0.120 m. Calculation, Example Written by MechStudies in Articles, Metalwork In this article, we will learn the moment of inertia of Solid or Hollow Sphere, along with examples, calculation, etc. The moment of inertia of a solid disc is, where M is the mass of the disc, and R is the radius. The moment of inertia of a hollow sphere or a spherical shell is often determined by the following formula I MR 2 We will look at a simple problem to further understand the usage of the formula. We can also use the moment of inertia for a hollow sphere ( 2 3 m a 2 ) to calcul ate the moment of inertia of a nonuniform solid sphere in which the density varies as ( r). The distance between the \(y\) and \(y'\) axis is available from the diagram.1) A DVD disc has a radius of 0.0600 m, and a mass of 0.0200 kg. The centroidal moment of inertia is calculated similarly using (10.2.10). Now, to solve such problem we need to use the right formula which is I (2/3)MR 2. Additionally, you can use this calculator to calculate the area, the centroid of the beam, and the section modulus.
the moment of inertia of a solid sphere is. This moment of inertia calculator determines the moment of inertia of geometrical figures such as triangles and rectangles. The area of the ring is found by subtracting the area of the inner circle from the area of the outer circle. Let us calculate the moment of inertia of a hollow sphere having a mass of 55.0 kg and a radius of 0.120 m. The moment of inertia of a sphere about its central axis and a thin spherical shell are shown.
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