## How do you find the center of gravity?

The center of gravity of an object is calculated by taking the sum of its moments divided by the overall weight of the object. The moment is the product of the weight and its location as measured from a set point called the origin.

## What is the moment of inertia of a solid sphere about its centre?

The moment of inertia of a solid sphere about an axis passing through the centre of gravity is 2/5MR2, then its radius of gyration about a parallel axis at a distance 2R from first axis is.

**What is the moment of inertia of a sphere of mass 20kg and radius 1/4 M about its diameter?**

So, moment of inertia is 0.5 kgm².

### What is the centre of gravity of a sphere?

A sphere is a uniform body with all points along it being at equal distance from its centre, so the centre of gravity is the centre of the sphere.

### What is the center of gravity of a sphere?

The geometrical center of triangle is the intersection of the Medians called Centeroid.. So center of gravity of Sphere lie at its center and Center of gravity lie at the Centroid of a triangle…

**When a sphere of moment of inertia about an axis through the center of gravity?**

The moment of inertia of a solid sphere about an axis passing through the centre radius is 1/2MR^(2) , then its radius of gyration about a parallel axis at a distance 2R from first axis is. where I=ICG=MI about an axis through the centre of gravity.

## How do you find the moment of inertia of a center of mass?

The moment of inertia is Iz=∑imi(x2i+y2i)=∫(x2+y2)dm….19–3Finding the moment of inertia.

Object | z-axis | Iz |
---|---|---|

Thin rod, length L | ⊥ rod at center | ML2/12 |

Thin concentric circular ring, radii r1 and r2 | ⊥ ring at center | M(r21+r22)/2 |

## What are the factors on which moment of inertia of a body depends Class 11?

The moment of inertia of a body is directly proportional to its mass and the distance of the particles of the body from the axis of rotation. Hence, the moment of inertia depends on mass and distance from the rotating axis, and force and density do not affect the moment of inertia of a body.

**What will be the radius of gyration for a solid sphere about a diameter whose radius is half meter 😕**

radius of gyration is the distance from the axis of rotation to the point where we suppose the whole mass is concentrated. hence, radius of gyration of a uniform solid sphere about its diameter is √(2/5)r.

### How to find moment of inertia of solid sphere?

How to Find Moment of Inertia of Solid Sphere A uniform solid sphere of mass M and radius R is taken. Moment of inertia is calculated about an axis passing through its centre. The solid sphere should be sliced to infinitesimally thin solid cylinders.

### How do you find the moment of inertia of a disk?

The moment of inertia of the disk about its center is Adding the moment of inertia of the rod plus the moment of inertia of the disk with a shifted axis of rotation, we find the moment of inertia for the compound object to be Now let’s examine some practical applications of moment of inertia calculations.

**Why is moment of inertia smaller at the center of mass?**

We would expect the moment of inertia to be smaller about an axis through the center of mass than the endpoint axis, just as it was for the barbell example at the start of this section. This happens because more mass is distributed farther from the axis of rotation.

## What is the moment of inertia of a thin spherical shell?

I(solid sphere) = kg m2 and the moment of inertia of a thin spherical shell is I(spherical shell) = kg m2 Show development of expressions Index Moment of inertia concepts HyperPhysics*****Mechanics R Nave Go Back Moment of Inertia: Sphere