* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 1.1 UCM AP
Survey
Document related concepts
Mechanics of planar particle motion wikipedia , lookup
Artificial gravity wikipedia , lookup
Lorentz force wikipedia , lookup
Speeds and feeds wikipedia , lookup
Relativistic angular momentum wikipedia , lookup
Coriolis force wikipedia , lookup
Velocity-addition formula wikipedia , lookup
Weightlessness wikipedia , lookup
Fictitious force wikipedia , lookup
Transcript
Uniform Circular Motion AP • Uniform circular motion is motion in a circle at the same speed • Speed is constant, velocity direction changes • the speed of an object moving in a circle is given by circumference 2 r r= radius of v T circle time T = period, time for 1 complete circle • Is called the 2 r v tangential velocity T Moon setting over Rio de Janerio Pictures every 6.5 minutes showing the moon is moving at a uniform speed Centripetal Acceleration • The direction of motion is changing so the object is accelerating v v f vi a t t • If you draw the vectors tailtail, v v f vi • the centripetal acceleration of the object is v2 ac r ac = centripetal acceleration (always to centre of circle) 2 ac Equations 2 r 2 v T a c r r 4 r 2 T r 2 2 2 4 r 2 T 2 On data sheet too! •the velocity vector is always directed along the tangent of the circle (at right angles to the acceleration vector) •centripetal means centreseeking, the acceleration vector always points to the centre of the circle •Acceleration is radially inward Centripetal Force • inertia tends to keep objects moving in a straight line, a force is needed to cause a circular motion (2nd Law of Motion) • the force causing the motion is called the centripetal force and it always acts towards the centre of the circle (parallel to the acceleration vector) Centrifuge Training F net m a 2 mv Fc r & 2 v ac r On data sheet NOT on data sheet • an object will move in a circle whenever a constant magnitude force acts on the object at right angles to its direction of motion • The force and acceleration are radially inward • The velocity is tangential • The string pulls ball towards the centre of the circle • 3rd Law of Motion states that a reaction force will act outward (ball pulls string) • this is sometimes called centrifugal force Important!!! • centripetal force is not a fundamental force like gravity, it is the net force acting on an object moving in a curved path • The force will not change the speed of the object because the force has NO component parallel to the velocity vector Example • A centrifuge for pilot training is 11 m in radius. At what speed must it rotate in order to inflict 7.0 g on a pilot? Solution 2 v ac r v ac r v 7.0 9.81m / s 11m 2 Frequency • sometimes speed is given in revolutions per minute (rpm) or revolutions per second (rps) • this is how many times the object goes around the circle in 1 minute or 1 second • frequency is the number of cycles per second measured in hertz (Hz) 1 1 Hz s second 1 T f 2 r v 2 rf T Example • Find the period of an object that rotates at 35.0 rps. 35.0circles 1circle 1s T T 0.0286s Example • A 3.50 kg object is swung in a 1.50 m radius horizontal circle at 40.0 rps (40.0 Hz). What magnitude force acts on the object? F net m a 2 4 rm Fc 2 T Solution 4 2r 2 m 4 rm F F net m a c 2 Fc 2 T T 1 f T 2 4 (1.50 m) (3.50 kg) Fc 2 2 2 so F 4 rmf (0.0250 s) Fc 3.32 x 105 N Effect of radius on speed and forces • all points on a rotating solid have the same period, but different speeds • because the inner points have smaller distances to travel, their speeds are less • the speed and force depends on the radius Rotating disc • NASA and other space agencies use this to help launch satellites • at the equator, the speed is about 1667 km/h, at Edmonton, it is about 900 km/h Angular displacement & velocity • The rotational displacement of a point, , in radians • 2 radians in 1 circle • Angular velocity, (lower case omega,) radians/s ave t Angular & linear speed • Linear speed = r • Linear speed is sometimes called tangential speed Period & angular speed 2 1 T f Direction of Angular velocity Equations of Rotational Motion 1 2 1 0 0t t x x0 vx 0t axt 2 2 2 0 t vx vx 0 a x t Example • A diver completes 1.5 rotations in 2.3 s. Determine the average angular speed of the diver Solution • 1.5 rotations x 2 rad = 9.425 radians ave 4.1rad / s t Example • A bullet is fired through 2 discs rotating at 99.0 rad/s. The discs are 0.955 m apart. The angular displacement between the holes is 0.260 rad. Calculate the speed of the bullet. Solution • = 99.0 rad/s. • D = 0.955 m • = 0.260 rad. ave t t = 2.626 x 10-3 s v = 364 m/s Small Angle Approximation • For small angles, < 0.5 rad, sin tan O