Question

A torque of 400 Nm acting on a body of mass 40 kg produces an angular acceleration of rad/s^2 calculate moment of inertia of the body​

Answer 1

$\checkmark$ Given:

A torque of 400 Nm acting on a body of mass 40 kg produces an angular

acceleration of 20 rad/s²

$\checkmark$ To Find:

Moment of Inertia of the body​

$\checkmark$ Solution:

We know that,

$\red{\bigstar \ \boxed{\rm I=\dfrac{\tau}{\alpha}}}$

Here,

• I = Moment of Inertia

• τ = Torque

• α = Angular Acceleration

According to the Question,

We are asked to find the Moment of Inertia of the body​

Given that,

A torque of 400 Nm acting on a body of mass 40 kg produces an angular

acceleration of 20 rad/s²

Therefore,

• τ = 400 Nm

• α = 20 rad/s²

Hence,

Substituting the above values,

We get,

$\blue{\implies \rm I=\dfrac{400}{20} \ Kgm^{2}}$

$\pink{\rm \implies I=20 \ Kgm^{2}}$

Therefore,

$\checkmark$ Moment of Inertia = 20 Kgm²

Answer 2

Given ,

Torque (T) = 400 N•m

Angular acceleration (α) = 20 rad/s²

We know that ,

Torque (T) is the product of moment of inertia and angular acceleration

It is denoted by " T "

$\boxed{ \sf{T = Moment \: of \: inertia \: (I) × angular \: acceleration \: (α)}}$

The SI unit of torque is N•m

It is vector quantity

Thus ,

400 = I × 20

I = 400/20

I = 2 Kg•m²

$\therefore \underline{ \sf{The \: moment \: of \: inertia \: is \: 2 \: kg. {m}^{2} }}$