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Hello students.
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So in this example we need to explain how do we get the calculated t and u values.
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For that, let us write t equals half m x .x.
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Square plus y dot square plus z dot square.
00:15
Now this is the formula in case of spherical polar coordinates for kinetic energy t.
00:20
Now let us write the spherical polar coordinates which is x equals b sine theta cause 5 .5.
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Now taking the derivative of this coordinate x with respect to time we get x dot equals b cos theta, cause phi multiplied by theta dot minus b sine theta theta sine phi phi dot.
00:54
So this is the derivative of x coordinate.
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Next we have y coordinate which is equal to to b sine theta multiply by sine 5.
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Now taking again the derivative with respect to time, y dot will become b, cos theta, sine phi multiplied by theta dot, plus b, sine theta, cause phi multiply by phi dot.
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This is the y coordinate and the derivative.
01:32
Now, z coordinate can be given as z equals b cause theta.
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So, its derivative, z -0 equals minus b, sine theta, multiply by theta dot.
01:53
So this is the third derivative.
01:56
So using these three coordinates, let us find the kinetic energy t, and put the values of x -dot, by, dot, z, dot, in the formula.
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So we get half m.
02:10
Firstly, x .d square will be b cos theta, cause phi, theta dot minus b, sine theta, sine theta, sine phi, phi, five, five dot square...