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Circular Motion Chapter 9 Circular Motion • Axis – is the straight line around which rotation takes place. • Internal Axis - is located within the body of the object. Circular Motion • Rotation – is the spin around the internal axis. • External axis – is outside the body of the object. Circular Motion • Linear speed - is distance/time • Since the outer edge of on object moving in a circle moves further it has greater linear speed. Circular Motion • Tangential speed – is the same as linear speed only with a circular motion. Circular Motion • Rotational speed - is the # of rotations/time • Tangential speed is approximately equal to radial distance x rotational speed. Circular Motion • IN ANY RIGIDLY ROTATING SYSTEM, ALL PARTS HAVE THE SAME ROTATIONAL SPEED. Circular Motion • Period (T) is the time it takes for one full rotation or revolution of an object. (measured in seconds) Circular Motion • Frequency (f) is the # of rotations or revolutions per unit of time. (measured in Hertz Hz). Circular Motion • T = 1/f • f = 1/T Circular Motion • Every object exerts gravitational force on every other object. • The force depends on how much mass the objects have and on how far apart they are. • The force is hard to detect unless at least one of the objects has a lot of mass. Circular Motion • Gravity is the force that keeps planets in orbit around the sun and governs the motion of the rest of the solar system. • Gravity alone holds us to the earth’s surface and explains the phenomenon of the tides. Reminders • Velocity is speed and the direction of travel. • Acceleration is the rate of change of velocity. • Force cause the acceleration of motion. • Work is done on an object to change the energy of the object. Some definitions • Centripetal means “center seeking” • Centrifugal means “center fleeing” Circular Motion • Consider a Ferris wheel. The cars on the rotating Ferris wheel are said to be in circular motion. Circular Motion • Any object that revolves about a single axis undergoes circular motion. • The line about which the rotation occurs is called the axis of rotation. • In this case, it is a line perpendicular to the side of the Ferris wheel and passing through the wheel’s center. Tangential speed • Tangential speed (vi) can be used to describe the speed of an object in circular motion. • The tangential speed of a car on the Ferris wheel is the car’s speed along an imaginary line drawn tangent to the car’s circular path. Tangential speed • This definition can be applied to an object moving in circular motion. • When the tangential speed is constant, the motion is described as uniform circular motion. Tangential speed • The tangential speed depends on the distance from the object to the center of the circular path. Tangential speed • For example, consider a pair of horses sideby-side on a carousel. • Each completes one full circle in the same time period, but the horse on the outside covers more distance than the inside horse does, so the outside horse has a greater tangential speed. Centripetal Acceleration • Suppose a car on a Ferris wheel is moving at a constant speed around the wheel. • Even though the tangential speed is constant, the car still has an acceleration. Centripetal Acceleration • a = vf - vi ________ tf - ti Centripetal Acceleration • Or put in words, centripetal acceleration is equal to linear speed squared divided by the radius. Speed • V = (2Πr) / T Centripetal Acceleration • Acceleration depends on a change in the velocity. • Because velocity is a vector, acceleration can be produced by a change in the magnitude of the velocity, a change in the direction of the velocity, or both. Centripetal Acceleration • The acceleration of a Ferris wheel car moving in a circular path and at constant speed is due to a change in direction. • An acceleration of this nature is called a centripetal acceleration. Centripetal Acceleration • The magnitude of a centripetal acceleration is given by the following equation. • Centripetal acceleration = (tangential speed)2 / radius of circular path Example • A test car moves at a constant speed around a circular track. If the car is 48.2 meters from the track’s center and has a centripetal acceleration of 8.05 m/s2 what is the car’s tangential speed? Solution • Given: r = 48.2 m ac = 8.05 m/s2 Unknown: vt = ? Solution • ac = vt2 / r • 8.05 m/s2 = vt2 / 48.2 m • vt = 19.7 m/s