Finding g with a Compound/Physical Pendulum: Plotting and Calculating

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To find the acceleration due to gravity using a compound pendulum, the formula T=2π*sqrt(I/mgh) is utilized. The discussion focuses on plotting the period T against the moment of inertia I, as the variable is changed by adjusting the mass along the rod. The relationship can be rearranged into the linear form y=mx+c, where T is on the y-axis and I on the x-axis. The gradient of the resulting line can then be used to calculate g. This method effectively links the physical properties of the pendulum to gravitational acceleration.
Pete2008
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Find the acceleration due to gravity using a compound/phyiscal pendulum. Using the formula: T=2pie*sqrt(I/mgh)

I understand how to find all the variables but to find g, i must plot a graph of T against something (Thats where i need help) and use the gradient of the line to calculate g.

so.

1.What do i plot against T
2.How would i calculate g from the gradient of the line

Thanks.
 
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Hi Pete and welcome to PF,

Firstly, what is the general equation of a straight line?
 
Hi,

The equation of a staright line is y=mx+c, and i guess that T would be the y axis/ the y part of the equation. Would the x-axis of the graph be I, because that's the variable I am changing by moving the mass along the rod?

Once I know the x and y part of the equation would it just be a case of rearanging the origional formula into y=mx+c?

Thanks
 
Last edited:
Pete2008 said:
Hi,

The equation of a staright line is y=mx+c, and i guess that T would be the y axis/ the y part of the equation. Would the x-axis of the graph be I, because that's the variable I am changing by moving the mass along the rod?

Once I know the x and y part of the equation would it just be a case of rearanging the origional formula into y=mx+c?

Thanks
Absolutely spot on :approve:
 
Thanks alot
 
Pete2008 said:
Thanks alot
No problem, I didn't do anything...:rolleyes:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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