You set a small eraser at a distance of 0.27 m from the center of a turntable yo

Question

You set a small eraser at a distance of 0.27 m from the center of a turntable you find in the attic and establish that when the turntable is turned on, the eraser travels in a circle with a constant tangential speed of 0.49 m/s. If your desk lamp projects a shadow of the apparatus on a wall which is the same size as the real apparatus, determine the following for the oscillatory motion of the eraser's shadow.

(a) period
s

(b) amplitude
m

(c) maximum speed
m/s

(d) magnitude of the maximum acceleration
m/s2

Explanation / Answer

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

You set a small eraser at a distance of 0.18 m from the center of a turntable you find in the attic and establish that when the turntable is turned on, the eraser travels in a circle with a constant tangential speed of 0.73 m/s. If your desk lamp projects a shadow of the apparatus on a wall which is the same size as the real apparatus, determine the following for the oscillatory motion of the eraser's shadow.

(a) period in s

(b) amplitude
in m

(c) maximum speed
in m/s

(d) magnitude of the maximum acceleration
in m/s2

Answer

The shadow excutes simple harmonic motion
w = V / R    where w is the angular frequency
w = 2 * pi * f = 2 * pi / T
(a) w = .73 / .18 = 4.06
T = 2 * pi / w = 1.55 sec
(b) A = .18     the amplitude
(c) Vm = .73 m/s     the maximum speed
(d) a = - A * w^2 = .18 * 4.06^2 = -2.97 m/s^2 (probably can omit minus sign)
Minus sign indicates acceleration towards the center of motion

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