What is the radial acceleration of a pendulum at a given angle?

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The discussion focuses on calculating the radial acceleration of a pendulum at a specific angle θ. It highlights that the radial acceleration depends on the velocity (v) of the pendulum bob and the length of the string (L). The velocity is not constant and varies with the angle θ, necessitating a function to express this relationship. Participants emphasize the need to derive the velocity function to accurately determine the radial acceleration. Understanding these dynamics is crucial for solving the problem effectively.
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A pendulum (with string length "L") and aball of mass "m" is pulled back to a horizontal position and then released. Assuming that θ is the angle between the string and the vertical, find (a.) the magnitude of the radial acceleration of this ball at an angle of θ as a function of m,g, L, and/or θ.


I think I found what "V" is but I am not completely sure.
 
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You know from the equation for centripetal acceleration that a is going to depend on v and the radius, which is L in this case. However, v is not constant, but rather is a function of theta. You need to find this function.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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