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the period is circumference / average linear velocity
the amplitude is the same as the circle radius, as this is the greatest distance away that the shadow can be from its central point.
you have the position of the shadow on the wall executing simple harmonic motion:
x(t) = Asin(wt) let's say, where A is the amplitude, w is the angular frequency, t is time.
the velocity is the first derivative with respect to time, v = dx/dt = wAcos(wt). look at the cos function, what value should it have for maximum velocity?
the acceleration is the second deriative. same idea as for maximum velocity.
the angular frequency = v / r
the amplitude is the same as the circle radius, as this is the greatest distance away that the shadow can be from its central point.
you have the position of the shadow on the wall executing simple harmonic motion:
x(t) = Asin(wt) let's say, where A is the amplitude, w is the angular frequency, t is time.
the velocity is the first derivative with respect to time, v = dx/dt = wAcos(wt). look at the cos function, what value should it have for maximum velocity?
the acceleration is the second deriative. same idea as for maximum velocity.
the angular frequency = v / r
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the Q is incomplete because the distance from the lamp to the peg and the peg to the wall makes a "triangle problem"
assume the lamp is very far away and the edge to edge shadow appears the diameter of the circle
the speed of the shadow seems to change even though the rotation "speed " of the wheel is constant
review sin and cosine graphs for a constant rate of angle change
assume the lamp is very far away and the edge to edge shadow appears the diameter of the circle
the speed of the shadow seems to change even though the rotation "speed " of the wheel is constant
review sin and cosine graphs for a constant rate of angle change