A metal rod of mass m and lenth l is rotating with w about an axis passing through o and normal to its length potential difference is bwl^2/6
Answers
The change in angular velocity is proportional to ω.
Explanation:
Correct statement:
A uniform metal rod of length 'L' and mass 'M' is rotating about an axis passing through one of the ends perpendiculars to the rod with angular speed 'ω' . If the temperature increases by t ° C then the change in its angular velocity is proportional to which of the following? (Coefficient of linear expansion of rod = α )
Solution:
The moment of inertia of a rod "I" = 1 / 3 M L^ 2
- As the temperature increases, the length of the rod also increases.
Thus new length of the rod L f =L ( 1 + α t )
New moment of inertia of rod = If = ML^3f / 3 = 1/3 ML^2 (1 + α t )^2
Let angular momentum decreases by Δ ω.
According to the principle of conservation of momentum.
Iω = If (ω - Δ ω)
Δ ω = If - I / If . ω
Δ ω α ω
Thus the change in angular velocity is proportional to ω.
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