A body of moment of inertia I = 0.80 kg m² about a fixed axis, rotates with constant angular velocity of 100 rad s⁻¹. Calculate its angular momentum L and the torque to sustain this motion. (Ans: 80 Js, 0)



Data Given:


Moment of inertia = `\I` = 0.80 kg m²

Constant angular velocity = ധ = 100 rad s⁻¹

To Find:


Angular Momentum  = `\vec L` = ?

Troque = `\vec T` = ?


Solution:


Using formula for Angular momentum L in terms of angular velocity  ധ and Moment of inertia `\I`

`\vec L` = `\I`ധ  

By putting values

`\vec L` = 0.80 kg m² ｘ100 rad s⁻¹  

`\vec L` = 80 kg m² rad s⁻¹  

or { as kg m² rad s⁻¹ = Js}

`\vec L` = 80 J s  

To find Torque T we have a formula in terms of angular acceleration  ∝ and Moment of inertia `\I`

`\vec T` = `\I` ∝

Since it is given that he body is moving with constant angular velocity, so angular acceleration will be zero i.e ∝ = 0 rad s⁻², thus 
`\vec T` = `\I` ∝

`\vec T` = 0.80 kg m² ｘ 0 rad s⁻²

`\vec T` = 0 N m

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