PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

CIRCULAR MOTION  Uniform Circular Motion  period, T : time for one complete revolution, unit: s  speed  is constant v = 2 p r/T (r: radius)  velocity is constantly changing (because direction is changing)

CIRCULAR MOTION  all turning objects have centripetal (center seeking) acceleration

CIRCULAR MOTION  centripetal acceleration , a c  = v 2 /r the greater the speed, the greater the centripetal acceleration  the smaller the radius of the turn, the greater the centripetal acceleration  a centripetal acceleration requires a centripetal force

CIRCULAR MOTION  no centrip etal force = no turning (linear motion)

CIRCULAR MOTION  centripetal force , F c = mv 2 /r any force can be a centripetal force : gravity (planets & moons) , friction (car turning a corner) , tension (ball on a string) , etc.

CIRCULAR MOTION  Frames of Reference inside a turning object , there seems to be a centrifugal (center fleeing) force pulling on objects

CIRCULAR MOTION  Frames of Reference outside the turning object , we see objects inside move in a straight line (inertia) , until they get pulled into the turn by centripetal force

CIRCULAR MOTION  centrifugal force only exists within the turning object’s frame of reference - it is a fictitious force

CIRCULAR MOTION  Frames of Reference things moving on a rotating object seem to be made to turn by the “ coriolis force ”

PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

QUIZ 3.1

A 50 kg child on a merry-go-round sits 2.0 m from the center and makes 2.0 complete revolution every second.

(a) Find the child's period.

(b) Find the child's tangential speed.

(c) Find the child's centripetal acceleration.

(d) Find the centripetal force on the child.

v = 2 p r/T a c = v 2 /r F c = mv 2 /r

PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

UNIVERSAL GRAVITATION  Newton's Law of Universal Gravitation : masses attract  gravity force is proportional to each mass  twice the mass = twice the force  gravity force is inversely proportional to the square of the distance between the masses  twice the distance = ¼ the force  distance measured from center of mass : point on a body around which mass is balanced

UNIVERSAL GRAVITATION  Newton's Law of Universal Gravitation:  F g = Gm 1 m 2 /r 2  F G : force of gravity, m: mass, r: distance between masses  G: universal gravitational constant, 6.67

× 10 -11 Nm 2 /kg 2  gravity is only significant for very large masses

UNIVERSAL GRAVITATION   acceleration due to gravity, g = Gm e /r 2 Also known as the gravitational field strength    m e : earth's mass (5.97

× 10 24 kg) r: distance from earth’s center (6.38

× 10 6 altitude) m + g is only 9.80 m/s 2 at sea level – it decreases as altitude increases  g is different on other planets & moons (it depends on the planet’s mass and radius)

UNIVERSAL GRAVITATION  Orbits: gravity provides the centripetal force    stable orbit: F c = F g orbit speed v = √Gm e /r orbit period T = 2 p r/v  geosynchronous orbit: T = 24.0 hrs, satellite stays over same position on earth

UNIVERSAL GRAVITATION  Orbits  always falling but never reaching the ground  "Weightlessness" is NOT gravity-less  no gravity = no orbit  weightless is no normal force

PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

ROTATIONAL MOTION  Rotational Motion : rotation around an internal axis  angle, q : how much an object has rotated,  unit: radian (rad)  2 p rad = 360º = 1 revolution (rev) angular velocity, w = Dq /t : rate of rotation, unit: rad/s  frequency: revolutions per second, unit: Hertz, Hz

ROTATIONAL MOTION  angular acceleration, a = Dw /t : rate of change in rotation, unit: rad/s 2  Rotational Motion & Circular Motion  for any point on a spinning object:  v = r w  a c = r w 2

ROTATIONAL MOTION  torque, t : rotating effect of a force, unit: Nm  t = Fdsin q  d: "torque arm" or "lever arm“  q: angle between F and d  torque direction: clockwise (c) or counterclockwise (cc)

ROTATIONAL MOTION   Torque is zero when q Torque is maximum = 0º or 180º when q = 90º

ROTATIONAL MOTION  Newton's Laws for Rotary Motion  A spinning object keeps spinning with constant angular velocity unless a net torque acts on it  A net torque causes an angular acceleration  For every action torque , there is an equal and opposite reaction torque

ROTATIONAL MOTION  Rotational Equilibrium : object is balanced, or moves with constant angular velocity, due to no net torque  S t c = S t cc d 1 d 2 F 1 F 2 F 2 d 2 = F 1 d 1

PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

UNIT 3 REVIEW v = 2 p r/T F g = Gm 1 m 2 /r 2 g = Gm p /r 2 m e = 5.97

× 6.38

× 10 6 10 m 24 w = Dq /t v = r w t = Fdsin q a c G = 6.67

v = √Gm kg a = = v Dw 2 a c = r w 2 /r /t S t c = S t cc p × /r 10 -11 F c = mv Nm 2 /kg 2 2 /r r e =