The direction of a centripetal force is toward the center of curvature, the same as the direction of centripetal acceleration. Just a few examples are the tension in the rope on a tether ball, the force of Earth’s gravity on the Moon, friction between roller skates and a rink floor, a banked roadway’s force on a car, and forces on the tube of a spinning centrifuge.

6.3: Centripetal Force Any force or combination of forces can cause a centripetal or radial acceleration.

In this section we examine the direction and magnitude of that acceleration. In uniform circular motion, the direction of the velocity changes constantly, so there is always an associated acceleration, even though the magnitude of the velocity might be constant.

6.2: Centripetal Acceleration We know from kinematics that acceleration is a change in velocity, either in its magnitude or in its direction, or both.

We begin the study of uniform circular motion by defining two angular quantities needed to describe rotational motion. In this chapter, we consider situations where the object does not land but moves in a curve.

6.1: Rotation Angle and Angular Velocity Projectile motion is a special case of two-dimensional kinematics in which the object is projected into the air, while being subject to the gravitational force, and lands a distance away.

In some ways, this chapter is a continuation of Dynamics: Newton's Laws of Motion as we study more applications of Newton’s laws of motion. We will therefore study not only motion along curves, but also the forces that cause it, including gravitational forces. Recall that Newton’s first law tells us that motion is along a straight line at constant speed unless there is a net external force.

6.0: Prelude to Uniform Circular Motion and Gravitation Many motions, such as the arc of a bird’s flight or Earth’s path around the Sun, are curved.

Using the formulae for centripetal acceleration and gravitational field strength, and the definition of angular velocity, derive an equation linking the orbital period of a planet to the radius of its orbit.ĥ.A planet of 1.5g revolves around the earth at a radius if 0.5 cm at a of frequency of 2 Hz. The centripetal force due to friction is 1.5 times the weight of the car. A 2000 kg car turns a corner, which is the arc of a circle, at 20kmh −1. Its year is 100 Earth years, and the distance from the star to the planet is 70 Gm from the star. A tennis ball of mass 10g is attached to the end of a 0.75m string and is swung in a circle around someone's head at a frequency of 1.5 Hz. The relationship between this 'magic' velocity and the magnitude of the centripetal force is as follows:į = m v 2 r Questions ġ. If you kept increasing the velocity and dropping it, there would come a point when it would land infinitely far away - it would go into orbit. If you gave it a little bit of velocity, it would still fall, but it would not land directly beneath its starting position. If you were to subject a stationary object to the centripetal force, it would simply fall. The object has a velocity, and will continue moving with this velocity unless acted on by the centripetal force, which is perpetually adding velocity towards the centre of the circle. Instead, the centripetal force accelerates the object with a constant magnitude in an ever-changing direction.

The object does not follow a circular path because two forces are balanced. It always acts towards the centre of the circle. There is only one force acting in circular motion, which is known as centripetal force. The key thing to note about circular motion is that there is no force pulling outwards from the circle, and there is no force pulling the moving object tangential to the circle. A car turning a corner might, briefly, move along the arc of a circle.

A conker on a string might move around my head in a circle. Some planets move in roughly circular orbits. Diagram showing the key variables involved in circular motion.

Circular motion