How to calculate the centrifugal impulse in the y direction?

How to calculate the component of the centrifugal impulse in the y direction created through travelling along a semicircle from the x axis to the negative x axis, 1st and second quadrants? I am trying to compute the total impulse taking the changing direction of the acceleration into account as a mass m travels along a semicircle at constant velocity v. Need to find the total impulse in the y direction if the semicircle is in the first two quadrants about the origin. Need equation in terms of velocity, radius, mass, time to complete semicircle path.

To calculate the component of the centrifugal impulse in the y-direction, we'll break it down into smaller parts. Assuming a constant velocity v and mass m, we'll use the following steps:

1. Find the centripetal acceleration (ac) in terms of v and radius (r): ac = v^2/r
2. Since the mass is moving in a semicircle, the acceleration vector will change direction. We'll resolve the acceleration into its x and y components using trigonometry.
3. Calculate the impulse (J) in the y-direction by integrating the y-component of the acceleration over time.

Here's the equation:

J_y = ∫[0,π] (m * v^2/r * sin(θ)) dθ

where θ is the angle from the x-axis to the position of the mass, ranging from 0 to π (covering the first two quadrants).

Simplifying and evaluating the integral, we get:

J_y = (2 * m * v^2)/r

This is the total impulse in the y-direction.

Is this correct?

• When I see the term "impulse," I assume it is sudden, such as would occur when a hammer hits something. Do you mean "force"? Commented Jul 30 at 1:24
• If you mean force and against vertical gravity, it's centripetal force minus gravity, the classic loop the loop roller coaster calculation. It's an equation using the sin of the angle. Commented Jul 30 at 5:19
• @user1683793 impulse is force times time and does not have to be sudden
– Dale
Commented Jul 30 at 18:59