Table of contents
- 0. Math Review31m
- 1. Intro to Physics Units1h 23m
- 2. 1D Motion / Kinematics3h 56m
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- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
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- 32. Electromagnetic Waves2h 14m
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- 35. Special Relativity2h 10m
16. Angular Momentum
Conservation of Angular Momentum
9:51 minutes
Problem 11.53dGiancoli Douglas - 5th edition
Textbook Question
Textbook Question(III) On a level billiards table a cue ball, initially at rest at point O on the table, is struck so that it leaves the cue stick with a center-of-mass speed v₀ and ω₀ a “reverse” spin of angular speed (see Fig. 11–41). A kinetic friction force acts on the ball as it initially skids across the table.
(d) If ω₀ is 10% larger than ,w_C i.e.,ω₀ = 1.10w_C, determine the ball’s cm velocity v_CM when it starts to roll without slipping. [Hint: The ball possesses two types of angular momentum, the first due to the linear speed v_CM of its cm relative to point O, the second due to the spin at angular velocity ω about its own cm. The ball’s total L about O is the sum of these two angular momenta.]
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Verified step by step guidance
1
Identify the relationship between the linear velocity (v_CM) and the angular velocity (ω) when the ball starts to roll without slipping. The condition for rolling without slipping is v_CM = Rω, where R is the radius of the ball.
Given that ω₀ is 10% larger than w_C, express ω₀ in terms of w_C: ω₀ = 1.10w_C.
Use the rolling without slipping condition to find w_C in terms of v₀ and R. From the condition v_CM = Rω, and knowing the initial conditions, set up the equation v₀ = Rw_C.
Substitute ω₀ from step 2 into the rolling condition to find v_CM when the ball starts to roll without slipping. Use the equation v_CM = Rω₀.
Calculate v_CM using the relationship v_CM = R * 1.10w_C and the expression for w_C from step 3.
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Textbook Question
The rotor (flywheel) of a toy gyroscope has mass 0.140 kg. Its moment of inertia about its axis is 1.20 * 10^-4 kg•m^2. The mass of the frame is 0.0250 kg. The gyroscope is supported on a single pivot (Fig. E10.51) with its center of mass a horizontal distance of 4.00 cm from the pivot. The gyroscope is precessing in a horizontal plane at the rate of one revolution in 2.20 s. (a) Find the upward force exerted by the pivot.
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