Two solid uniform disks of eqaul mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks are r1 < r2. A force F is applied to each disk at its edge for the same amount of time. Assume that friction at pulley axis is negligible. What statement is true about the kinetic energy (K) and magnitude of angular momentum (L) of the disks?

Engineering

Physics

Conservation of Angular Momentum

Question

Two solid uniform disks of eqaul mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks are r₁ < r₂. A force F is applied to each disk at its edge for the same amount of time. Assume that friction at pulley axis is negligible. What statement is true about the kinetic energy (K) and magnitude of angular momentum (L) of the disks?

L₁ < L₂ and K₁ > K₂

L₁ = L₂ and K₁< K₂

L₁ < L₂ and K₁ < K₂

L₁ < L₂ and K₁ = K₂

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L₁ = $\frac{{Fr}_{1}}{\frac{1}{2} {mr}_{1}^{2}}$ = $\frac{2 F}{{mr}_{1}}$    L₂ = $\frac{2 F}{{mr}_{2}}$
ω₁ = $\frac{2 Ft}{{mr}_{1}}$          ω₂ = $\frac{2 Ft}{{mr}_{2}}$
E₁ = $\frac{1}{2}$ I₁ω₁²            E₂ = $\frac{F^{2} t^{2}}{m}$
= $\frac{F^{2} t^{2}}{m}$
L₁ = I₁ω₁        L₂ = Ftr₂
L₁ = Ftr₁
so,   E₁ = E₂     &   L₁ < L₂

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