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 solve for T in the first one.
is that correct?
Calculate I total for the three particles
(I = sum of 1/2 m r^2 for all three).
Then sum torques=I * angacceleration
solve for ang acceleration.
displacement=1/2 * angacceleration*time+wi*t
where wi=angacceleartion*5sec
solve for time from the displacement equation.
thanks bob!
Your approach is on the right track, but there are a few things to clarify.
To find the time it takes for the system to perform one full rotation, you can use the equation:
T = 2π / ω,
where T is the period (time for one full rotation), and ω is the angular velocity.
To find the angular velocity, you correctly mentioned using the formula:
ω = αt,
where α is the angular acceleration, and t is the time.
However, to find the angular acceleration, you need to use the formula:
α = τ / I,
where τ is the torque applied to the system, and I is the system's total moment of inertia.
So, to summarize the process:
1. Calculate the torque (τ) applied to the system by summing up the torques applied by each individual force on the system.
2. Calculate the system's total moment of inertia (I) using the given coordinates and masses of the particles.
3. Find the angular acceleration (α) by dividing the torque (τ) by the moment of inertia (I).
4. Use the formula ω = αt to find the angular velocity (ω) after 5 seconds.
5. Finally, plug the value of ω into the formula T = 2π / ω to find the time taken for one full rotation.
Remember to double-check your calculations and units to ensure accuracy in the final result.