Rotational Motion and Rotational Motion and the Law of Gravitythe Law of Gravity

Causes of Circular MotionCauses of Circular Motion

Force That Maintains Circular Force That Maintains Circular MotionMotion

Objects that travel in circular paths Objects that travel in circular paths have forces that maintain that have forces that maintain that circular motioncircular motion– Called Force that maintains circular Called Force that maintains circular

motion (Fmotion (Fcc))

– Measured in Newtons (N)Measured in Newtons (N)– Must be directed toward the center of Must be directed toward the center of

the circular paththe circular path

Force That Maintains Circular Force That Maintains Circular MotionMotion

Force that maintains circular motion Force that maintains circular motion = mass * centripetal acceleration= mass * centripetal acceleration– FFcc=ma=macc

Force that maintains circular motion Force that maintains circular motion = mass * (tangential speed)= mass * (tangential speed)22/radius/radius– FFcc=mv=mvtt

22/r/r Force that maintains circular motion Force that maintains circular motion

= mass * radius * (angular speed)= mass * radius * (angular speed)22

– FFcc=mr=mrωω22

Describing the Motion of a Rotating Describing the Motion of a Rotating SystemSystem

Inertia is often misinterpreted as a Inertia is often misinterpreted as a forceforce– Centrifugal forceCentrifugal force

Not a forceNot a force

In order to maintain circular motion, In order to maintain circular motion, the force that maintains circular the force that maintains circular motion must overcome inertiamotion must overcome inertia

Newton’s Law of Universal Newton’s Law of Universal GravitationGravitation

Gravitational force – the mutual force of Gravitational force – the mutual force of attraction between particles of matterattraction between particles of matter

Every pair of objects experience gravitational Every pair of objects experience gravitational attraction between themattraction between them

Most objects do not notice this attractionMost objects do not notice this attraction– Objects’ masses are too small and the distance between Objects’ masses are too small and the distance between

them is too largethem is too large– Gravity is only noticeable over short distances when one Gravity is only noticeable over short distances when one

object is very large (planet or moon-sized)object is very large (planet or moon-sized)– When both objects are very large, the gravity is When both objects are very large, the gravity is

noticeable at larger distances (sun and planets noticeable at larger distances (sun and planets gravitational attraction keeps the planets in orbit)gravitational attraction keeps the planets in orbit)

Newton’s Law of Universal Newton’s Law of Universal GravitationGravitation

Gravitational force = constant * Gravitational force = constant * (mass 1 * mass 2)/(distance between (mass 1 * mass 2)/(distance between center of masses)center of masses)22

FFgg=Gm=Gm11mm22/r/r22

G=6.673*10G=6.673*10-11-11 Nm Nm22/kg2/kg2 Gravitational force is concentrated at Gravitational force is concentrated at

the center of a spherical massthe center of a spherical mass