Question

derive an expression of moment of interia​

Answer 1

Answer:

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• ᴛʜᴇ ᴍᴏᴍᴇɴᴛ ᴏғ ɪɴᴇʀᴛɪᴀ ᴀʙᴏᴜᴛ ᴛʜᴇ ᴇɴᴅ ᴏғ ᴛʜᴇ ʀᴏᴅ ᴄᴀɴ ʙᴇ ᴄᴀʟᴄᴜʟᴀᴛᴇᴅ ᴅɪʀᴇᴄᴛʟʏ ᴏʀ ᴏʙᴛᴀɪɴᴇᴅ ғʀᴏᴍ ᴛʜᴇ ᴄᴇɴᴛᴇʀ ᴏғ ᴍᴀss ᴇxᴘʀᴇssɪᴏɴ ʙʏ ᴜsᴇ ᴏғ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟ ᴀxɪs ᴛʜᴇᴏʀᴇᴍ. ɪ = ᴋɢ ᴍ². ɪғ ᴛʜᴇ ᴛʜɪᴄᴋɴᴇss ɪs ɴᴏᴛ ɴᴇɢʟɪɢɪʙʟᴇ, ᴛʜᴇɴ ᴛʜᴇ ᴇxᴘʀᴇssɪᴏɴ ғᴏʀ ɪ ᴏғ ᴀ ᴄʏʟɪɴᴅᴇʀ ᴀʙᴏᴜᴛ ɪᴛs ᴇɴᴅ ᴄᴀɴ ʙᴇ ᴜsᴇᴅ.

Answer 2

Explanation:

OVERVIEW AND DEFINITION

Moment of inertia aka angular mass or rotational inertia can be defined w.r.t. rotation axis, as a quantity that decides the amount of torque required for a desired angular acceleration or a property of a body due to which it resists angular acceleration. The formula for moment of inertia is the “sum of the product of mass” of each particle with the “square of its distance from the axis of the rotation”.

• The formula of Moment of Inertia is expressed as I = Σ miri2.

DERIVATION :-

The physical object is made of the small particles. The Mass Moment of Inertia of the physical object is expressible as the sum of Products of the mass and square of its perpendicular distance through the point that is fixed (A point which causes the moment about the axis passing through it).

We denote the Mass Moment of Inertia by I

Let’s take consideration of a physical body that has a mass of m.

It composes of small particles whose masses are

M1 , m2,m3. etc. respectively.

The perpendicular distance of each particle from the line as shown figure is: K

From the above statement, the Mass Moment of Inertia for the whole body will be as:

I = m1(k1)² +m2(k2)² +M3(k3)² +...........so on

From the concept of center of mass and center of gravity, the mass of a body that we assume to be concentrated at a point.

The mass at that point will be m and theperpendicular distance of point from the fixed line is k

∴hence,

m1(k1)² +m2(k2)² +M3(k3)² = Mk²

so, I = mk²

here K is the radius of gyration.

⚕️ NONEXISTENT ⚕️