# Rotational Motion of a pendulum

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1. Jul 27, 2016

### xxphysics

1. The problem statement, all variables and given/known data
A pendulum is made of a bob dangling from a lightweight string of length ℓ. The bob is pulled sideways so that the string makes an angle θi with respect to the vertical, then released.

As it swings down, what is the rotational speed of the bob as a function of the changing angle θ? Use the notation l for the length of the string ℓ.
Express your answer in terms of the the variables m, l, θ, θi, and acceleration due to gravity g.

2. Relevant equations
h = l(cosθ - cosθi)
v=(2gh)^1/2
w = v/l
3. The attempt at a solution
I got w = ((2ghl(cosθ - cosθi))^(1/2))/l , but that was not correct. Are my equations wrong? Thanks

2. Jul 27, 2016

### haruspex

How come there is still an h in there?

3. Jul 27, 2016

### xxphysics

oh sorry ignore that. I entered it without it

4. Jul 27, 2016

### haruspex

Then your answer looks ok to me. Do you know what the official answer is? Or do you enter it into a software package that simply says yes or no? If the second, maybe you need to simplify it a bit by cancellation, leaving l in the denominator only.

5. Jul 27, 2016

### xxphysics

I enter it on the computer. It gave me the hint "The correct answer involves the variable \texttip{\theta _}{theta_}, which was not part of your answer.", but I guess my computer isn't able to read that portion of the tip ? Not sure, but thank you

6. Jul 27, 2016

### xxphysics

How would you simplify it further since for the numerator the square root needs to be taken ?

7. Jul 27, 2016

### haruspex

Sounds like it needs you to enter it as cos(θ) etc., not cosθ. Or maybe you did.
√x/x=1/√x