- #1
Nate
- 4
- 2
- Homework Statement
- A pendulum is made from two identical uniform thin rods and hung from a point O. These each have a length 𝐿 and a mass 𝑚. The moment of inertia of a thin rod of length 𝐿 and a mass 𝑚 around its centre is 𝐼=𝑚𝐿^2/12.
Part A:Given that 𝐿=31.0cm and 𝑚=100g, what is the moment of inertia of the whole T about the point O?
Part B: What is the potential energy of the pendulum if it is at an angle 𝜃=30.0° to the vertical, if its potential energy is taken to be zero at 𝜃=0°?
Part C: By working out the total energy when the pendulum is in motion, and remembering that this must remain constant, or by using the angular equivalent of Newton's Second Law, find the period of small oscillations of the pendulum.
- Relevant Equations
- For Part A a relevant equation is the parallel axis theorem, I=I𝖢𝗈𝖬+𝑚l^2
For Part B a relevant equation is potential energy (PE)=mgh
For Part C a relevant equation for simple harmonic motion is ¨x =−𝜔^2x
My answer to part A is correct but for Part B I got an incorrect answer of 0.204J. My working out is sent as an attachment.
Part A:
Part B:
Part C:
Part A:
Part B:
Part C: