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Physics help with angular velocity and inertia problem?
Two automobiles both of 1200kg and both traveling at 29km/h collide on a frictionless icy road. They were initially moving on parallel paths in opposite directions, with a center-tocenter distance of 1m. In the collision, the automobiles lock together, forming a single body of wreckage; the moment of inertia of this body about its center of mass is 2.5*10^3 kg*m^2.
What is the angular velocity of the wreck?
Calculate the kinetic energy before the collision and after the collision. What is the change in kinetic energy?
1 Answer
- NCSLv 76 years ago
angular momentum L = Σ mvr = Σ Iω
initial L = 2 * 1200kg * 29km/h * 1m/s / 3.6km/h * 0.5m = 9667 kg·m²/s
final L = 9667 kg·m²/s = 2500kg·m² * ω
ω = 3.9 rad/s ◄ angular velocity
initial KE = 2 * ½ * 1200kg * (29/3.6 m/s)² = 77 870 J
final KE = ½Iω² = ½ * 2500kg·m² * (3.9rad/s)² = 18 690 J
ΔKE = -59 180 J ≈ -59 kJ
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