I have this number where they give me the coordinates of 3 particles and the mass of each one of them. Afterwards, there's a force applied on 2 of those particles and they ask me to calculate the systems total moment of inertia. But then they ask me this:
If the system goes from rest and that the forces from c) are applied for 5 seconds and after that 5 seconds no more forces are exerted, how much time does the system take to perform one full rotation.
So I think I'll find the answer using
T = 2pie/w, where I'll find w by first finding my angular acceleration a = t/I
from where I can find w using w = at. Then I would just use T in f = 1/T.
is that correct?
Yes, your approach to find the time it takes for the system to perform one full rotation seems correct. Let me explain the steps in more detail:
1. Find the angular acceleration (α):
- Given that forces are applied on two particles, you need to calculate the total net torque acting on the system.
- Use the formula τ = Iα, where τ is the total torque and I is the total moment of inertia of the system.
- Rearrange the formula to find α: α = τ/I.
2. Calculate the angular velocity (ω):
- Given that the forces are applied for 5 seconds, use the formula α = Δω/Δt.
- Rearrange the formula to find ω: ω = αt.
3. Determine the time period (T):
- The time it takes for one full rotation is the period of rotation, denoted as T.
- Use the formula T = 2π/ω.
4. Calculate the time for one full rotation:
- Plug the value of ω into the formula T = 2π/ω to find the time required for one full rotation.
Remember to check the units and ensure that they are consistent throughout the calculations.