A uniform disc is spinning about geometrical axis in free space. Its temperature is increased by ∆T. The fractional change in its angular velocity is (α is coefficient of linear expansion)

Question

A uniform disc is spinning about geometrical axis in free space. Its temperature is increased by ∆T. The fractional change in its angular velocity is (α is coefficient of linear expansion) (A) 2 α Δ T (B) -2 α Δ T (C) - α Δ T (D) α Δ T

Tardigrade Admin · Accepted Answer

Angular momentum remains constant I ω = const. (Δ l/l)+ (Δ ω/ω)=0 2 α Δ T + (Δ ω/ω)=0 ∴ (Δ ω/ω) = -2 α Δ T

Q. A uniform disc is spinning about geometrical axis in free space. Its temperature is increased by ∆T. The fractional change in its angular velocity is ( $α$ is coefficient of linear expansion)

$2 α Δ T$

$- 2 α Δ T$

$- α Δ T$

$α Δ T$

Angular momentum remains constant
$I ω = co n s t .$
$\frac{Δ l}{l} + \frac{Δ ω}{ω} = 0$
$2 α Δ T + \frac{Δ ω}{ω} = 0 ∴ \frac{Δ ω}{ω} = - 2 α Δ T$

Q. A uniform disc is spinning about geometrical axis in free space. Its temperature is increased by ∆T. The fractional change in its angular velocity is (α is coefficient of linear expansion)

2αΔT

−2αΔT

−αΔT

αΔT