hw1_ocw

# hw1_ocw - accelerations Use a rotating cylindrical...

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16.61 Handout #3 Prof. J. P. How Feb 6, 2003 Prof. J. Deyst Due: Feb 13, 2003 16.61 Homework Assignment #1 1. A wheel of radius 2 r is moving along a horizontal surface such that its hub travels at a speed v = 3 At (where A is a constant). Find the expression for the acceleration a ( t ) of the point that was at the top of the wheel at time t = 0. Use the FARM approach, and clearly define all coordinate frames of interest in the problem. Give your final answer in terms of the components in the inertial frame. Using A=1/3, plot a ( t ) for the first 10 seconds. Does your result make physical sense? 2. Given a Frame B rotating with respect to inertial space at rate Ω, use the transport theorem to show that I B ˙ ˙ Please provide a physical interpretation of this result. What are the implications of this result when using the FARM approach? 3. For the 3 cases on Page 2-4 in the notes, use the formula on Page 1-7 in the notes to calculate the absolute accelerations for the mass. Use these results to specify the magnitude and direction of the Coriolis
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Unformatted text preview: accelerations. Use a rotating cylindrical co-ordinate frame, as outlined on Page 2-7. Conﬁrm that these results agree with the answers given in class. 4. An new experimental vehicle travels due North from the equator to the Pole along a railway track. The vehicle moves at a constant speed v relative to the Earth (which you can assume is ﬁxed, but rotating at rate Ω). Determine the Coriolis acceleration a cor as a function of latitude θ . If v = 500 km/h, what is the magnitude of a cor at the equator and at the pole? 5. Who was the Coriolis eﬀect named after? Describe something that you commonly do in which the Coriolis eﬀect plays an important role. 1...
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