Moment of inertia of an annular disc along one of its diameters is half of the moment of inertia along its central axis.

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## What is the moment of inertia of an annular disc?

Moment of inertia of an annular disc along one of its diameters is half of the moment of inertia along its central axis.

**How do you find the MOI of annular disc?**

Moment Of Inertia Of Annular Disc

- We will start by recalling the moment of inertia expression which is given as; dI = r2 dm.
- We can then write a new expression for Izz. It will be;
- Now we need to find the total mass of the annular disk.
- In the next step, we will substitute the above values in equation 2, which is.

**What is moment of inertia of a circle?**

Moment of inertia of a circle or the second-moment area of a circle is usually determined using the following expression; I = π R4 / 4. Here, R is the radius and the axis is passing through the centre. This equation is equivalent to I = π D4 / 64 when we express it taking the diameter (D) of the circle.

### What is the moment of inertia of ring and disc?

What is the moment of inertia of the ring about its center? I = mR2 . This is the same as the moment of inertia of a single body at distance R from the center. Let’s let the mass of the disc be m, and its radius be R.

**What is the moment of inertia of a hollow sphere?**

The moment of inertia of the hollow sphere is 0.528 kg.

**What is the moment of inertia of Triangle?**

For a uniform triangular plate, the moments of inertia are taken to be about the vertical axis passing through the plate’s center of mass. The moment of inertia of a uniform triangular plate about the vertical axis passing through its center of mass is proportional to the sum of the squares of the sides and the mass.

#### What is the moment of inertia of solid sphere?

dm = ρ dV, where ρ is the density of the solid cylinder and dV is the volume.

**What are the moment of inertia of a solid sphere and hollow sphere?**

Stay updated with the Physics questions & answers with Testbook. Know more about Rotational Motion and ace the concept of Rotational Inertia….Detailed Solution.

Shape | Axis of rotation | Moment of inertia |
---|---|---|

Solid sphere | through center | I = 2 5 m r 2 |

Hollow sphere | through center | I = 2 3 m r 2 |

**What is moment of inertia of a solid and hollow sphere?**

## What is the moment of inertia of annular disc?

Moment of inertia of an annular disc that is uniform and having mass (m), thickness (t), inner radius (R 1) and outer radius (R 2) is expressed as; Here, we have to consider that the disc is rotating about an axis passing through the centre. 1. We will start by recalling the moment of inertia expression which is given as;

**What is the moment of inertia of a uniform angular?**

The Moment of inertia of a uniform angular with mass m, thickness t and inner and outer radius as R1 and R2 respectively can be expressed as: Here, we consider that the disc is rotating about an axis passing through the centre. 1.

**What is the second moment of area of a shape?**

The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area for a shape is easier to be calculeted…

### How do you find the Izz of an annular disk?

Izz = ½ πpt [ R2⁴ – R1⁴ ] …………… (Equation 1) Also, it can be expressed as [ R2² + R1²] [ R2² – R1²]. Izz = ½ πpt [ R2² + R1²] [ R2² – R1²] …………….. (Equation 2) 3. Next step is to find the total mass of the annular disk.