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When a body is in uniform circular motion, the force on it changes the direction of its motion but not its speed. For a body moving in a circle of radius r {\displaystyle r} at a constant speed v {\displaystyle v} , its acceleration has a magnitude a = v 2 r {\displaystyle a={\frac {v^{2}}{r}}} and is directed toward the center of the circle.
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
Gravity field surrounding Earth from a macroscopic perspective. Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors.
Gravity F = mg does work W = mgh along any descending path. In the absence of other forces, gravity results in a constant downward acceleration of every freely moving object. Near Earth's surface the acceleration due to gravity is g = 9.8 m⋅s −2 and the gravitational force on an object of mass m is F g = mg.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
and are equal in magnitude and opposite in direction. So, the body that exerts will be pushed backward.) [5] Newton's three laws of motion were the first to accurately provide a mathematical model for understanding orbiting bodies in outer space. This explanation unified the motion of celestial bodies and the motion of objects on Earth.
The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g (also called acceleration due to gravity). By Newton's Second Law the force F g {\displaystyle \mathbf {F_{g}} } acting on a body is given by: F g = m g . {\displaystyle \mathbf {F_{g}} =m\mathbf {g} .}
In particular, Newton determined that the acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law. Further, Newton realized that the acceleration of a body due to gravity is proportional to the mass of the other attracting body. [33]