This is known as the Schwarzschild radius. It is approximately 2.95 km per solar mass.
As the radius of rotation decreases, the number of revolutions of a rubber stopper increases. This is due to the conservation of angular momentum - with a smaller radius, the rotational speed must increase to maintain the same angular momentum.
"Rate of change" means that you divide something by time ("per unit time" or "per second"), so you would use the units of angular momentum, divided by seconds.I am not aware of any special name for this concept.
It would increase due to the conservation of angular momentum.
Momentum affects a boomerang's flight by determining its speed and direction. When thrown with sufficient force and spin, the boomerang's momentum helps it maintain its rotational motion and return to the thrower. The conservation of momentum and angular momentum also play a role in the boomerang's flight path.
Assuming a circular orbit for simplicity, the magnitude of the angular momentum is rmv - that is, the radius of the orbit times the mass times the velocity. I'll leave the details of the calculations to you; basically you have to look up:Earth's, or the Moon's, orbital radius (the distance from Sun to Earth vs. the distance from Earth to the Moon);The mass of the orbiting object;Its velocity in orbit.Then you must divide one by the other, since I assume it's the ratio you are interested in.
To change the speed without changing the angular momentum, you can change the radius of the rotating object. This is because angular momentum is the product of an object's moment of inertia, its mass, and its angular velocity. By adjusting the radius while keeping the other factors constant, you can alter the speed without affecting the angular momentum.
Angular momentum is defined as the moment of linear momentum about an axis. So if the component of linear momentum is along the radius vector then its moment will be zero. So radial component will not contribute to angular momentum
mass, velocity, and radius.
The black hole property that determines the Schwarzschild radius of the black hole is that it has mass but no angular momentum nor electric charge.
The formula for calculating angular momentum in terms of kilogram meters squared per second is: Angular Momentum Mass x Velocity x Radius
As the radius of rotation decreases, the number of revolutions of a rubber stopper increases. This is due to the conservation of angular momentum - with a smaller radius, the rotational speed must increase to maintain the same angular momentum.
When a spinning skater pulls in her arms to turn faster, her angular momentum is conserved. Angular momentum is the product of an object's moment of inertia and its angular velocity. By pulling her arms in, the skater decreases her moment of inertia, causing her angular velocity to increase in order to maintain a constant angular momentum. This is similar to the principle of conservation of angular momentum seen in other rotating systems.
"Rate of change" means that you divide something by time ("per unit time" or "per second"), so you would use the units of angular momentum, divided by seconds.I am not aware of any special name for this concept.
To calculate her angular momentum, you would need to know her moment of inertia (which depends on both her mass and how this mass is distributed relative to the axis of rotation), her velocity (speed at which she travels in a circular path), and the radius of the circle she is skating. You would use the formula for angular momentum, which is given by the equation: L = I * ω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.
As a star shrinks, its angular speed typically increases due to the conservation of angular momentum. This means that as the star's radius decreases, its rotation rate speeds up in order to conserve the total angular momentum of the system.
Angular momentum about the axis of rotation is the moment of linear momentum about the axis. Linear momentum is mv ie product of mass and linear velocity. To get the moment of momentum we multiply mv by r, r the radius vector ie the distance right from the point to the momentum vector. So angular momentum = mv x r But we know v = rw, so angular momentum L = mr2 x w (w-angular velocity) mr2 is nothing but the moment of inertia of the moving body about the axis of rotation. Hence L = I w.
The velocity of a rotating object is directly proportional to its radius. As the radius increases, the velocity also increases to maintain angular momentum. Mathematically, this relationship is described by the equation v = rω, where v is the linear velocity, r is the radius, and ω is the angular velocity.