Question

The moment of inertia of a wheel is 1000kg msquare

Answer 1

≡QUESTION≡

Moment of inertia of a wheel is 1000 kgm2. At a given instant, its angular velocity is 10 rad/sec. After the wheel rotates through an angle of 100 radians, the angular velocity of the wheel is 100 rad/sec. The torque applied on wheel in nm is?

                                                     

║⊕ANSWER⊕║

GIVEN

Moment of inertia = 1000 kg m²

Angular velocity 1 ( ω₁ ) = 10 rad / sec

Angle = 100 radians

Angular velocity 2 ( ω₂ ) = 100 rad / sec

ω² - ω1² = 2 ∝ Ф

ω₁ is angular velocity 1

ω₂ is is angular velocity 2

α is angular acceleration

Ф is the angle formed

∝ = ω² - ω1²/2Ф

∝ = (100)² - (10)²/2 * 100

∝ = 49.5 rad/s²

T=I * α  

T is the torques

I is the Inertia

α  is the angular acceleration

T = 1000 *  49.5

  = 4.95 × 10⁴  Nm

                                                     

Answer 2

The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr 2.