Solving Force and Inertia in Equation of Motion

In summary, the force applied to a piston connected to a flywheel can be calculated using the equation F = ma, with a being the angular acceleration. This can be rearranged to find the angular acceleration of the flywheel by multiplying the resultant force by the radius of the flywheel and dividing by its moment of inertia.
  • #1
a.mlw.walker
148
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So I have a piston connected to a flywheel. If i push the piston with a force F, how does the equation of motion look? I'm not confident about putting inertias into the same equation as accelerations?

F = ma

F = I(theta'')

The force is changing with time.

EDIT:

So i have just realized that T = Ia, a is angular acceleration.

So if i find resultant force of piston acting along line of tangential velocity on the flywheel, then moultiply it by r of the flywheel,

Fr = Ia, then rearrange for a and i have angular acceleration of flywheel?
 
Last edited:
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  • #2
Hi a.mlw.walker! :smile:

(have a tau: τ and a theta: θ and an omega: ω and an alpha: α :wink:)
a.mlw.walker said:
So i have just realized that T = Ia, a is angular acceleration.

So if i find resultant force of piston acting along line of tangential velocity on the flywheel, then moultiply it by r of the flywheel,

Fr = Ia, then rearrange for a and i have angular acceleration of flywheel?

That's right …

the standard linear equations apply, with τ I θ ω and α instead of F m s v and a. :wink:
 

What is force and inertia in the equation of motion?

Force and inertia are two important concepts in physics that are used to describe the motion of objects. Force is a push or pull on an object that can cause it to accelerate, change direction, or change shape. Inertia is the resistance of an object to changes in its state of motion.

What is the equation of motion?

The equation of motion is a mathematical representation of the relationship between an object's position, velocity, acceleration, and time. It is typically written in the form of F=ma, where F is the force applied to an object, m is its mass, and a is its acceleration.

How do you solve for force in the equation of motion?

To solve for force in the equation of motion, you first need to know the values for mass and acceleration. Then, you can simply plug those values into the equation F=ma and solve for F. It is important to make sure that the units for mass and acceleration are consistent, as force is typically measured in Newtons (N).

What is the relationship between force and acceleration in the equation of motion?

According to the equation of motion, force and acceleration are directly proportional. This means that if you increase the force applied to an object, its acceleration will also increase. Similarly, if you decrease the force, the acceleration will decrease as well.

How does inertia affect the equation of motion?

Inertia plays a crucial role in the equation of motion, as it determines how an object will respond to an applied force. Objects with greater inertia will require more force to accelerate, while objects with less inertia will require less force. This is why it is often easier to push a lighter object than a heavier one.

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