This sounds overcomplicated to me compared to an explanation I once heard. Suppose you are orbiting a planet, you have a gun with a single bullet, and you want to maximize your total energy after firing the bullet backwards. At what point in the trajectory should you shoot the bullet? Since energy is conserved, you want to minimize the bullet’s energy. Because KE = mv^2, you have maximal ability to decrease (or increase) the bullet’s energy when its KE is already highest, and because KE+U is constant, this is at the lowest point in your trajectory.
I don’t think so. The difference in the gravitational field between the bottom point of the swing arc and the top is negligible. The swing isn’t an isolated system, so you’re able to transmit force to the bar as you move around.
There’s a common explanation you’ll find online of how swings work by you changing the height of your center of mass, which is wrong, since it would imply that a swing with rigid bars wouldn’t work. But they do.
There are two completely distinct ways to swing on a swing- You can rotate your body relative to the seat-chain body at the same frequency as your swinging but out of phase, or move your center of mass up and down the chain at twice the frequency. The power of the former is ~ torque applied to chain \* angular velocity, the power output of the latter is radial velocity of your body \* (angular velocity ^2 \* chain length).
To get to any height, you have to switch from one to the other once the angular velocity ^2 term dominates- this is why learning to swing is so unintuitive.
This sounds overcomplicated to me compared to an explanation I once heard. Suppose you are orbiting a planet, you have a gun with a single bullet, and you want to maximize your total energy after firing the bullet backwards. At what point in the trajectory should you shoot the bullet? Since energy is conserved, you want to minimize the bullet’s energy. Because KE = mv^2, you have maximal ability to decrease (or increase) the bullet’s energy when its KE is already highest, and because KE+U is constant, this is at the lowest point in your trajectory.
I don’t remember where I first heard this.
Is this also how swinging on swings works? How does swinging on swings work exactly? Huh.
I don’t think so. The difference in the gravitational field between the bottom point of the swing arc and the top is negligible. The swing isn’t an isolated system, so you’re able to transmit force to the bar as you move around.
There’s a common explanation you’ll find online of how swings work by you changing the height of your center of mass, which is wrong, since it would imply that a swing with rigid bars wouldn’t work. But they do.
The actual explanation seems to be something to do with changing your angular momentum at specific points by rotating your body.
There are two completely distinct ways to swing on a swing- You can rotate your body relative to the seat-chain body at the same frequency as your swinging but out of phase, or move your center of mass up and down the chain at twice the frequency. The power of the former is ~ torque applied to chain \* angular velocity, the power output of the latter is radial velocity of your body \* (angular velocity ^2 \* chain length).
To get to any height, you have to switch from one to the other once the angular velocity ^2 term dominates- this is why learning to swing is so unintuitive.