Special Case: Uniform Circular Motion is the (constant) “angular velocity” positive if CCW So x and y change sinusoidally Direction angle changes at a constant rate x-axis
Period of Motion Period, T, is the time it takes time to go If it goes all the way around once, the angle changes by (rad) If it goes all the way around once, the distance traveled is
Special Case: Uniform Circular Motion An object moves in a circle of constant radius, r, with constant speed, v. Is the object accelerating? Consider ways of ID’ing acceleration: physical intuition: force needed, jerk felt math:
Acceleration What is the acceleration of the object at Consider the average acceleration from just before to just after: Generally: centripetal acceleration is
Magnitude of Acceleration Same r and larger v yields: Same v and smaller r yields: Same T and larger r yields:
Example What is the speed and acceleration of the Earth in orbit? r = 93,000,000 mi = 1.5X10 11 m T = 1yr = 3.156X10 7 s = 30,000 m/s = 0.0059 m/s 2 huge circle –
Newton’s 1 st Law An object at rest remains at rest, object in motion remains in uniform motion (i.e. constant velocity, no change in speed nor direction) unless acted on by a net external force. demos
Inertia Inertia is the word used to describe this tendency: It is NOT a resistance to motion It is a resistance to CHANGE in motion Inertia is a property of matter. Define mass: if an object has inertia, then it has mass.
Centripetal Force – 1 st Law Recall: 1 st Law An object in motion will continue no change Can only continue in circle if
Newton’s Second Law An net external force can change an object's velocity, can accelerate it. The force required is proportional to the acceleration, and in the same direction. The force required is also proportional to the object’s mass.
Newton’s Second Law Improved What is meant by “net” external force? take all the external forces, and add them as vectors. the resultant is the net force. Notation: means sum Note: there may be several forces; add them. there is only one acceleration.
Centripetal Force – 2 nd Law Recall: centripetal acceleration An object moving in a circle is accelerating Recall: 2 nd Law in order for object to accelerate The acceleration is toward center, so centripetal force is
Centripetal Force – Examples What force holds each in circular motion? A ball swung around on a string: You, as you rotate around with Earth’s surface: Amusement-park ride: you’re plastered to the wall and the floor drops out Coin on a turntable
Newton’s Third Law “For every action, there is an equal and opposite reaction” Better said: “For every FORCE, there is an equal and opposite reaction FORCE.” If A pushes on B, then B pushes back on A at the same time.
Newton’s 3 rd Law For every FORCE, there is an equal and opposite reaction FORCE. If I try to push the door open, the door pushes back on me, making it hard to open a door in a wheelchair. If the Earth pulls down on me with a gravitational force, then I pull up on the Earth with exactly the same size force!
More on the 3 rd Law The object pushes back, even if it accelerates. when you shoot a gun you accelerate bullet forward you can feel it push _________ on you “recoil” when you catch a ball you accelerate it backward (to stop it) you can feel it push __________ on you
3 rd Law Reaction on What? The “action” FORCE and the “reaction” FORCE don’t act ON the same thing. If the action force is Earth’s gravity pulling on ME, then the reaction force is me pulling on the Earth. If the action force is your behind pushing down on the chair, then the reaction force is the chair pushing up on your behind (keeping you from falling)