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In Newtonian mechanics, gravity provides the centripetal force causing astronomical orbits. One common example involving centripetal force is the case in which a body moves with uniform speed along a circular path. The centripetal force is directed at right angles to the motion and also along the radius towards the centre of the circular path.
The normal force is actually the sum of the radial and tangential forces. The component of weight force is responsible for the tangential force (when we neglect friction). The centripetal force is due to the change in the direction of velocity. The normal force and weight may also point in the same direction.
Here the centripetal force is the gravitational force, ... The formula is dimensionless, ... the orbital velocity for a circular orbit with radius ...
Every central force can produce uniform circular motion, provided that the initial radius r and speed v satisfy the equation for the centripetal force = () If this equation is satisfied at the initial moments, it will be satisfied at all later times; the particle will continue to move in a circle of radius r at speed v forever.
The only requirement is that the central force exactly equals the centripetal force, which determines the required angular velocity for a given circular radius. Non-central forces (i.e., those that depend on the angular variables as well as the radius) are ignored here, since they do not produce circular orbits in general.
This equation relating the two radial forces can be understood qualitatively as follows. The difference in angular speeds (or equivalently, in angular momenta) causes a difference in the centripetal force requirement; to offset this, the radial force must be altered with an inverse-cube force.
Upper panel: Ball on a banked circular track moving with constant speed ; Lower panel: Forces on the ball.The resultant or net force on the ball found by vector addition of the normal force exerted by the road and vertical force due to gravity must equal the required force for centripetal acceleration dictated by the need to travel a circular path.
Applying the centripetal force formula F = mv 2 /r results in ... The virial mass and radius are generally defined for the radius at which the velocity dispersion is ...