Conservation of Angular Momentum
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AP Physics C: Mechanics › Conservation of Angular Momentum
A satellite in space has initial rotational inertia $I_i=120,\text{kg·m}^2$ and spins at $\omega_i=1.5,\text{rad/s}$. It deploys solar panels, increasing inertia to $I_f=300,\text{kg·m}^2$ with negligible external torque. Angular momentum is conserved during deployment. Considering the given conditions, calculate the new speed of rotation when the configuration changes.
0.60 rad/s
1.50 rad/s
-0.60 rad/s
3.75 rad/s
Explanation
This question tests AP Physics C: Mechanics skills, specifically the conservation of angular momentum. Angular momentum is conserved in a closed system without external torques; it is calculated as the product of rotational inertia and angular velocity (L = Iω). In this scenario, a satellite deploys solar panels, increasing its moment of inertia from 120 to 300 kg·m², which causes the angular velocity to decrease proportionally. Choice A is correct because L_initial = I_i·ω_i = 120·1.5 = 180 kg·m²/s, and ω_final = L_initial/I_final = 180/300 = 0.60 rad/s. Choice B is incorrect as it represents the inverse calculation (300/120)·1.5, a common error when students confuse the relationship between I and ω. To help students: Use the ice skater analogy - extending arms increases I and decreases ω. Practice problems with changing configurations, emphasizing that L = Iω remains constant while I and ω change inversely.