Circular Motion

What is Circular Motion? Uniform Circular Motion is motion along a circular path in which there is no change in speed, only a change in direction. Constant velocity tangent to path. Constant force toward center.

What if the string breaks? The ball moves tangent to path, NOT outward as might be expected.The ball moves tangent to path, NOT outward as might be expected. When the central force is removed, ball continues in straight line. Centripetal force is needed to change direction v

Circular Motion and Force If an object stays in its path…it must have a net force responsible This force is called… CENTRIPETAL FORCE centrum "center" and petere “go to” or “seek” So, it’s a “center – seeking” force **This is not a new force !** It is the F net responsible for circular motion!

Examples Roller coasters & rotating platform rides Swinging an object on a string Car going around a curve Planetary objects-moon, satellites, etc.

Spin Cycle on a Washer How is the water removed from clothes during the spin cycle of a washer? Think carefully before answering... NO. Actually, it is the LACK of a force that allows the water to leave the clothes through holes in the circular wall of the rotating washer.

Centripetal Acceleration Consider ball moving at constant speed v in a horizontal circle of radius R at end of string tied to peg on center of table. (Assume zero friction.) R v Force F c and acceleration a c toward center. F g = F N FcFc FNFNFNFN Fg

Centripetal acceleration is… The acceleration of an object in uniform circular motion. The a c always points toward the center.

Finally put it all together… So, for centripetal force…

Remember The circumference of a circle –C = 2πr r

Using Period, T, to find velocity The time it takes an object to make a complete revolution is the period. –During this time, it travels a distance equal to the circumference of the circle –Remember, v = ∆d/∆t –So, v = 2πr/T

“Critical Velocity” Is the minimum/maximum velocity needed to maintain the circular path You can consider vertical motion (like a satellite) or horizontal motion (like a car) –For example, what is the fastest you can go around a curve in your car without losing control or, what is the minimum speed a satellite needs to stay in orbit?

Vertical Critical Velocity The minimum velocity required for an object (like a satellite) to travel a circular path of radius, r. How? – at min. velocity, F c = F w (forces are balanced) –mv 2 /r = mg –v 2 = rg V c = √(rg)

Horizontal Critical Velocity The maximum velocity an object (like a car) can safely round a curve How? – at max. speed, F c = F f (forces are balanced) –mv 2 /r = μF N –mv 2 /r = μmg –v 2 = rμg – V c = √(rμg)

How many g’s? The g-force references the acceleration of the object relative to free-fall –The ratio of an object’s acceleration to the acceleration due to gravity To determine the number of “g’s” an object experiences: object’s acceleration gravitational accel. (9.8 m/s 2 )

What to remember What circular motion is- be able to recognize it Newton’s Second Law- you will see it again! That velocity has direction and speed Centripetal acceleration deals with the change in direction Things that effect centripetal force are mass, velocity, and the distance from the center (radius)

Let’s do some Calculations 1)What is an object’s centripetal acceleration if it travels 22 m/s around a circular path with a 12 cm radius?

2)It takes a 615 kg race car 14.3 seconds to travel at a uniform speed around a circular track with a 50 meter radius. a) What is the acceleration of the car? b) What average force must the tires exert on the track to produce this acceleration?

3) Calculate the centripetal force of an object that weighs 49 N traveling in a circular path (radius of 1200 mm) if it rotates 150 revolutions per minute.

You try one… 4) An athlete whirls a 7 kg hammer tied to the end of a 1.3 meter chain in a horizontal circle. The hammer moves at a rate of 1 revolution per second. a) What is the centripetal acceleration of the hammer? b) What is the tension in the chain?