Question

Check correctness of torque = moment of inertia × angular acceleration​

Answer 1

Answer:

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Explanation:

Answer 2

Answer:

The given statement is correct.

Torque = moment of inertia × angular acceleration

Explanation:

• To produce angular acceleration for an object, toque is required. It is based on the distribution of mass on the object.
• The distribution is based on the moment of inertia.

Torque = moment of Inertia × angular acceleration

τ = I α

• τ = torque (N m)
• I = moment of inertia (kg m²)
• α = angular acceleration (radian/s²)

Derivation:

The angular acceleration is produced in the body when torque acts on the body.

Angular acceleration (α) = dω / dt

The linear acceleration will depend on the distance r₁, r₂, r₃.........rₙ

Consider a particle which has mass m₁ , distance r₁ which has linear velocity v₁

Linear acceleration of the particle = α₁ = r₁α ..................(1)

Force acting on the particle = F₁ = m₁r₁α   .......................(2)

Moment of Force F₁ about the axis is given as

τ₁ = F₁r₁     ........................................(3)

Substituting the value of F₁

τ₁ = m₁r₁²α   ...................................(4)

Total torque is given as:

τ₁ + τ₂ + τ₃+..........................τₙ

τ =  m₁r₁²α +  m₂r₂²α +  m₃r₃²α+..................... mₙrₙ²α

τ =  (m₁r₁² + m₂r₂² + m₃r₃²+..................... mₙrₙ²)α

τ  =  (Σmr²) α  ..................................(5)

Where I = Σmr²

τ  = I α  .................................(6)

The above equation shows the relationship between torque, moment of inertia and angular acceleration. Therefore,

τ  = I α . The statement is correct.

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