One of the many little experiments I performed at home that you can also do.
I attached a clip to the edge of a table and a string, such that the string is free to swing like a pendulum.
You can tie any object to the end of the string. I tied a nail cuter.
I then measured the distance from the top of the string to the bottom of the nail cutter, centre of it and the very top of it.
We can predict the time it should take for a full period (swing back and forth) with some maths:
Centripetal acceleration,a, = v^2 / r
The acceleration the pendulum is under is always that of gravity, therefore g = v^2 / r
The velocity the pendulum is the distance covered per X amount of time,
v = circumference / period, = 2 π r / T
Rearranging both formulas for 'V' , at end up with a formula (square root of (4 π^2 r / g) = T ) )
simplified, it ends up as
We now calculate the time if should take for each of the radii' ; from bottom, middle, top
Write down the predicted time for each.
-I knew that the actual time would be slightly less than the predicted one, due to air friction, and I took into account in my formula that Sydney's gravity is +/- 9.797, not 9.81
You can Google and roughly find the value of "g" for your city.
With that written down, begin the experiment:
Pull the mass up not too high and let it swing. Once it reaches a peak height, beginning to time and wait for it to do that 10 times before stopping the timer. (The first time it comes back to that peak height being swing no. 1)
Do that at least 3 times then add all the results up. Divide the sum of the results by 10 x amount of times repeated.
You now have the average period of for the pendulum. Compare that with the predicted periods for each length. Again, keep in mind that the value you got would be slightly higher than the correct one, due to air friction and human error.
My value was definitely closest to the centre of mass.
I attached a clip to the edge of a table and a string, such that the string is free to swing like a pendulum.
You can tie any object to the end of the string. I tied a nail cuter.
I then measured the distance from the top of the string to the bottom of the nail cutter, centre of it and the very top of it.
We can predict the time it should take for a full period (swing back and forth) with some maths:
Centripetal acceleration,a, = v^2 / r
The acceleration the pendulum is under is always that of gravity, therefore g = v^2 / r
The velocity the pendulum is the distance covered per X amount of time,
v = circumference / period, = 2 π r / T
Rearranging both formulas for 'V' , at end up with a formula (square root of (4 π^2 r / g) = T ) )
simplified, it ends up as
Where L = r = radius
We now calculate the time if should take for each of the radii' ; from bottom, middle, top
Write down the predicted time for each.
-I knew that the actual time would be slightly less than the predicted one, due to air friction, and I took into account in my formula that Sydney's gravity is +/- 9.797, not 9.81
You can Google and roughly find the value of "g" for your city.
With that written down, begin the experiment:
Pull the mass up not too high and let it swing. Once it reaches a peak height, beginning to time and wait for it to do that 10 times before stopping the timer. (The first time it comes back to that peak height being swing no. 1)
Do that at least 3 times then add all the results up. Divide the sum of the results by 10 x amount of times repeated.
You now have the average period of for the pendulum. Compare that with the predicted periods for each length. Again, keep in mind that the value you got would be slightly higher than the correct one, due to air friction and human error.
My value was definitely closest to the centre of mass.