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Unformatted text preview: Physics 130 Sample Exam 4 Short Answer section. Please answer all of the short answer questions. 1. Compute the total angular momentum and kinetic energy that the earth has due to its rotation about an axis that runs from the north to the south pole. Compute the total angular momentum and kinetic energy that the earth has in its circular orbit. (Note: You will need to look up the mass and radius of the earth). ω = 2 π rad 24 hrs ⋅ 3600 s / hr = 7.27 × 10 − 5 rad / s I sphere = 2 5 MR 2 = 2 5 ⋅ 5.98 × 10 2 4 kg ⋅ (6.37 × 10 6 m ) 2 = 9.71 × 10 3 7 kgm 2 L = I ω = 9.71 × 10 3 7 kgm 2 ⋅ 7.27 × 10 − 5 rad / s = 7.06 × 10 3 3 kgm 2 / s E = 1 2 I ω 2 = 1 2 9.71 × 10 3 7 kgm 2 ⋅ (7.27 × 10 − 5 rad / s ) 2 = 2.566 × 10 2 9 J For orbital motion v = 2 π r t = 2 π ⋅ 1.5 × 10 1 1 365 days ⋅ 24 hrs / day ⋅ 3600 s / hr = 2.989 × 10 4 m / s p = mv = 5.98 × 10 2 4 kg ⋅ 2.989 × 10 4 kgm / s L = rp sin θ = 1.5 × 10 1 1 m ⋅ 5.98 × 10 2 4 kg ⋅ 2.989 × 10 4 m / s = 2.68 × 10 4 0 kgm 2 / s E = 1 2 mv 2 = 1 2 5.98 × 10 2 4 kg ⋅ (2.989 × 10 4 m / s ) 2 = 2.671 × 10 3 3 J 2. A force of 100 N is applied to a bar that can rotate around one end. Compute the torque that is produced and be sure to indicate the direction of the torque. The bar responds by accelerating with an angular acceleration of 1 rad/s 2 . What is the moment of the inertia of the bar? 100 N 60˚ τ = r × F τ = rF sin θ = r ⋅ 100 N ⋅ sin 60 τ = I α I = τ α = r ⋅ 100 N ⋅ sin 60 1 rad / s 2 The torque points out of the paper. 3. A solid disk with a cord wrapped around it unwinds without slipping. Use energy methods to show that after it has fallen a distance h, its linear velocity is v = 4 gh 3 Starting with energy conservation E i = E f + mgh = ( 1 2 I ω 2 + 1 2 mv 2 ) + I = 1 2 mr 2 ω = v r mgh = 1 2 ( 1 2 mr...
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This note was uploaded on 09/27/2010 for the course ASD 2456 taught by Professor Jojo during the Spring '10 term at Brooklyn Law School.
 Spring '10
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