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For a particle moving in the x-y plane, the position can be written in polar coordinates as rrr, where r = x² + y² and F = cos 0+ sin 0. Show that the velocity can be written as v = rî+roo, where the unit vector is orthogonal to r.

For a particle moving in the x-y plane, the position can be written in polar coordinates as rrr, where r = x² + y² and F = cos 0+ sin 0. Show that the velocity can be written as v = rî+roo, where the unit vector is orthogonal to r.

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For a particle moving in the x-y plane, the position can be written in polar coordinates as rrr, where r = x² + y² and F = cos 0+ sin 0. Show that the velocity can be written as v = rr+roo, where the unit vector is orthogonal to r. A cylinder of mass M and radius R is rolling along a surface without slipping at a speed v. Show that the total kinetic energy of the cylinder is T = ³/Mv².
Transcribed Image Text:For a particle moving in the x-y plane, the position can be written in polar coordinates as rrr, where r = x² + y² and F = cos 0+ sin 0. Show that the velocity can be written as v = rr+roo, where the unit vector is orthogonal to r. A cylinder of mass M and radius R is rolling along a surface without slipping at a speed v. Show that the total kinetic energy of the cylinder is T = ³/Mv².
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