Check correctness of torque = moment of inertia × angular acceleration
Answers
Answer:
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Explanation:
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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