Circular Motion

Two types of Spin Rotation occurs when object spins around internal axis that is attached to object. – E.g. Merry-go-round, rotating platforms at amusement parks, Earth on North South axis, cartwheels, flips and peroets Revolution occurs when object spins around external axis that is not attached to object. – E.g. Planets around sun, cars on track or turn, ball on string, moons around planets

Rules for Rotation Outside has greater linear speed than inside (m/s) Outside and inside have same angular speed (rotations per minute) Need more friction to stay on outside rim compared to inside of object. New set of variables and kinematic equations (  ) Spin is conserved

Rules for Revolution In order for an object to revolve or partially revolve (turn) there must be a net inward directed force (centripetal force). Centripetal force changes direction but NOT speed. F centripetal = m v tangential 2 / radius of turn – Centripetal force greater for sharp, small radii turns. – Centripetal force greater for greater speeds around turns. – Centripetal force greater for more massive objects making a turn Centripetal force is NOT a new force, only direction

Centrifugal Farce A centrifugal force is a center fleeing force that would be directed outwards from a turn or circle. Usually due to inertia of object Examples – Bug in can – Thrown to outside of car when turning – Lopsided Earth in orbit – Centrifuge – Amusement Park Ride

Artificial Gravity Result of rotating tubular object and throwing objects inside to outside wall of tube. – Faster rotation results in greater “gravity” – Larger diameter results in lesser “gravity” – In a space station “Gravity” at center of tube is zero while on edges could be 1 g.

Centrifugal Farce Centrifugal force would be a center fleeing or outward force Bug whirled around in can example – Thrown to outside – Bug will claim that force is acting on it but outside viewer knows bug is simply following inertial path Centrifuge example – Separates materials according to its inertia/mass – Should be called an inertiafuge! In above cases there is no interaction thus no outward force Centrifugal force

Artificial Gravity on Space Station Bug in spinning tire – Faster spin means thrown against wall harder – Larger tire means thrown against wall softer – In center of axle, bug will simply rotate and not be thrown at all For rotating circular space station – Faster spin means you would gain “weight” – As move toward center you would lose “weight”, at center you’re weightless

Circular motion requires an inward force Examples – Water in bucket-road on car – Ball on string-car door on driver – Motorcycle in motordrome -Earth on moon Inward forces for above are – Bucket on water-friction from road – Tension of string-normal force from door – Normal force from track-gravity These forces are said to be in the centripetal direction and thus centripetal forces

Inward force causes change in direction but not speed. Examples – Water in bucket -road on car – Ball on string-car door on driver – Motorcycle in motordrome -Earth on moon Centripetal or inward force in all of these examples is perpendicular to direction object is traveling at that moment. These centripetal forces cannot do work on moving object and the speed will remain constant. Inward or centripetal force changes direction of object but not speed.

Check Question A block of ice slides along a smooth surface. Will forces in the following directions affect the speed, direction or both of the block? 1.Force is in same direction of motion 2.Force is in opposite direction of motion 3.Force is perpendicular to direction of motion a)Direction only is affected b)Speed only c)Speed and direction

The magnitude of the inward force depends on the mass, radius of curvature, and velocity Centripetal force increases proportionally w/ mass made to move in circle Centripetal force increases as the square of the tangential speed Centripetal force decreases linearly w/ increase of radius of curvature F centripetal = mass x tangential velocity 2 / radius =mv 2 /r where v 2 /r is sometimes called the centripetal acceleration. Just Newton’s 2 nd law w/ a special acceleration

Check Question A ball is whirled on the string in a horizontal circle. Which of the following changes will increase the centripetal force needed to keep the ball moving in a circle? a)Increasing the speed the ball is whirled b)Increasing the mass of the ball c)Increasing the radius of the circle the ball is making d)A and B only e)All of these

Odds and Ends Tangential vs rotational or angular speed – Tangential speed is a linear speed measured in meters/ second and the like – Angular speed is measured in radians/second – Tangential speed increases as move away from center, angular speed remains constant Centripetal vs. angular acceleration – Centripetal acceleration is a linear acceleration measured in m/s/s and directed towards the middle of the circle (a=v 2 /r) – Angular acceleration is measured in radians/sec/sec, and measures increase or decrease in spin rate

Check Questions A ball is whirled around on a string as shown from above in the picture. If the string is cut at the position shown, what is the path of the ball? A B C D E