Rotational Motion of a pendulum

[xxphysics]

Homework Statement

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.

Homework Equations

h = l(cosθ - cosθi)
v=(2gh)^1/2
w = v/l

The Attempt at a Solution

I got w = ((2ghl(cosθ - cosθi))^(1/2))/l , but that was not correct. Are my equations wrong? Thanks

 

[haruspex]

I got w = ((2ghl(cosθ - cosθi))^(1/2))/l

How come there is still an h in there?

 

[xxphysics]

How come there is still an h in there?

oh sorry ignore that. I entered it without it

 

[haruspex]

oh sorry ignore that. I entered it without it

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.

 

[xxphysics]

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.

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

 

[xxphysics]

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.

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

 

[haruspex]

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

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

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

√x/x=1/√x