5: Kinetic energy for polar coordinates and/or rotating systems (a) Practice Assignment 4, please write a formula for the particle's kinetic energy in terms of m and/or † and/or o and/or r and/or ø. Symbols like i, ÿ, væ, and vy should NOT show up anywhere in your answer. Consider a particle of mass m moving in the xy plane. Using the results of (b) and rewrite the kinetic energy in terms of the z component of angular momentum. Also, eliminate i from the kinetic energy and rewrite it in terms of the radial component of the linear momentum (i.e. Pr = mr). Use the results of the previous problem to eliminate o from the kinetic energy (I'm having you do this because as we go on in mechanics we'll talk less and less about velocity and more and more about momentum.) Finally, the angular momentum of an object rotating about an axis is L = I3, (c) where I is the moment of inertia, and the kinetic energy is Iw². Rewrite the kinetic energy in terms of the angular momentum and moment of inertia.
5: Kinetic energy for polar coordinates and/or rotating systems (a) Practice Assignment 4, please write a formula for the particle's kinetic energy in terms of m and/or † and/or o and/or r and/or ø. Symbols like i, ÿ, væ, and vy should NOT show up anywhere in your answer. Consider a particle of mass m moving in the xy plane. Using the results of (b) and rewrite the kinetic energy in terms of the z component of angular momentum. Also, eliminate i from the kinetic energy and rewrite it in terms of the radial component of the linear momentum (i.e. Pr = mr). Use the results of the previous problem to eliminate o from the kinetic energy (I'm having you do this because as we go on in mechanics we'll talk less and less about velocity and more and more about momentum.) Finally, the angular momentum of an object rotating about an axis is L = I3, (c) where I is the moment of inertia, and the kinetic energy is Iw². Rewrite the kinetic energy in terms of the angular momentum and moment of inertia.
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Transcribed Image Text:5: Kinetic energy for polar coordinates and/or rotating systems
(a)
Practice Assignment 4, please write a formula for the particle's kinetic energy in terms of
m and/or † and/or o and/or r and/or ø. Symbols like i, ÿ, væ, and vy should NOT show
up anywhere in your answer.
Consider a particle of mass m moving in the xy plane. Using the results of
(b)
and rewrite the kinetic energy in terms of the z component of angular momentum. Also,
eliminate i from the kinetic energy and rewrite it in terms of the radial component of the
linear momentum (i.e. Pr = mr).
Use the results of the previous problem to eliminate o from the kinetic energy
(I'm having you do this because as we go on in mechanics we'll talk less and less about
velocity and more and more about momentum.)
Finally, the angular momentum of an object rotating about an axis is L = I3,
(c)
where I is the moment of inertia, and the kinetic energy is Iw². Rewrite the kinetic energy
in terms of the angular momentum and moment of inertia.
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