Physics 1710 Chapter 6—Circular Motion

Answer:Answer:

a = a = ∆v/∆∆v/∆t t a = (112 m/s)/(2.5 sec) = a = (112 m/s)/(2.5 sec) = 44.8 m/s44.8 m/s22

Thrust = forceThrust = forceF = ma = (1800. kg)(44.8 m/s F = ma = (1800. kg)(44.8 m/s 2 2 ) ~ 81 kN) ~ 81 kN

Physics 1710Physics 1710 Chapter 6—Circular Chapter 6—Circular Motion Motion

11′ Lecture:′ Lecture: • The net force on a body executing circular motion The net force on a body executing circular motion is equal to the mass times the centripetal is equal to the mass times the centripetal acceleration of the body. acceleration of the body. FFcentripetalcentripetal = = m m aaccentripetalentripetal

•aacentripetalcentripetal = = v v 22/ R/ R [toward the center]; [toward the center]; aa = - = -ωω22 rr

• In non-inertial frames of reference one may sense In non-inertial frames of reference one may sense fictitious forces.fictitious forces.

• At At terminal velocityterminal velocity the velocity-dependent the velocity-dependent resistive forces balance the accelerating forces so resistive forces balance the accelerating forces so that no further acceleration occurs.that no further acceleration occurs.


Centripetal Acceleration:Centripetal Acceleration:


x = r cos x = r cos θθyy = r sin = r sin θθ

vvxx = (dr/dt) cos = (dr/dt) cos θθ- r sin - r sin θθ(d (d θ/dt)θ/dt) vvyy = (dr/dt) sin = (dr/dt) sin θθ+r cos +r cos θθ(d (d θ/dt)θ/dt) Let (dr/dt) = 0Let (dr/dt) = 0 vvxx = - r = - r ω ω sin sin θθ

vvyy = +r = +r ω ω cos cos θθ

aaxx = dv= dvxx /dt= d(- r /dt= d(- r ω ω sin sin θ)/dt θ)/dt = = r r ωω22cos cos θ- θ- r r ω ω sin sin θ(d ω/dt)θ(d ω/dt)

aayy = dv= dvyy /dt= d(r /dt= d(r ω ω cos cos θ)/dt θ)/dt = -= -r r ωω22sin sin θ+ θ+ r r ω cosω cos θ(d ω/dt)θ(d ω/dt)

a a = = - ω- ω22 r + r + r r (d (d vvtangentialtangential /dt) /dt)

θθvvxx

vvyy

Centripetal Acceleration:Centripetal Acceleration:


a a centripetalcentripetal = = - v - v 22 / r / r

aa tangentialtangential = = r r (d v(d vtangentialtangential /dt)/dt)

F F = m = m a a

F F centripetalcentripetal = m a = m a centripetalcentripetal = = - mv - mv 22 / r / r

θθvvxx

vvyy

Demonstration: Ball on a StringDemonstration: Ball on a String


FFcentripetalcentripetal

rr

mm

vv

FFcentripetal centripetal = m v = m v 22/r /r

An athlete swings a 8 kg “hammer” around An athlete swings a 8 kg “hammer” around on a 1.2 m long cable at an angular on a 1.2 m long cable at an angular frequency of 1.0 revolution per second. How frequency of 1.0 revolution per second. How much force must he exert on the hammer much force must he exert on the hammer throw handle?throw handle?

Physics 1710 — Physics 1710 — e-Quize-Quiz

Answer Now !

1 2 3 4

7%

57%

22%

15%

1.1. About 12. NAbout 12. N




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Demonstration: Ball on a StringDemonstration: Ball on a String


FFcentripetalcentripetal

rr

mm

vv

v = 2v = 2π r/T = 2(3.14) (1.2 m)/(1.0 sec) = 7.5 π r/T = 2(3.14) (1.2 m)/(1.0 sec) = 7.5 m/sm/s

FFcentripetal centripetal = m v = m v 22/r = (8.0 kg)(7.5 m/s)/r = (8.0 kg)(7.5 m/s)22/(1.2 /(1.2 m) m)

= 378 N ~ 380 N= 378 N ~ 380 N

Demonstration: Demonstration: Marble in a bottleMarble in a bottle


Why does the marble stay up on Why does the marble stay up on the side?the side?

No Talking!No Talking!Think!Think!

Confer!Confer!

Peer Instruction Peer Instruction TimeTime

Why does the marble stay up on the Why does the marble stay up on the side?side?


Satellites in OrbitSatellites in Orbit


Which orbit is most like that of the Space Which orbit is most like that of the Space Shuttle?Shuttle?

No Talking!No Talking!Think!Think! Confer!Confer!

Peer Instruction Peer Instruction TimeTime

Physics 1710Physics 1710 Unit 1—Review Unit 1—Review

11223344

Satellite Motion:Satellite Motion:• h ~ 100 km , h ~ 100 km , RR⊕ ⊕ ~ 6300 km~ 6300 km

•FFgg= G Mm/ r = G Mm/ r 22 GravitGravityy

• FFgg = F = Frr = mv = mv 22/r /r

• v = v = √[GM/r] = √[GM/(R√[GM/r] = √[GM/(R⊕ ⊕ + h)]~ √[GM/R+ h)]~ √[GM/R⊕ ⊕ ]]

= √[gR= √[gR⊕ ⊕ ]= √[(9.8 m/s]= √[(9.8 m/s22)(6.3 x10)(6.3 x1066m)m) ]= ]=

7.9x107.9x1033 m/s m/s

~17,600 mph~17,600 mph

• Why do the shuttle astronauts appear Why do the shuttle astronauts appear

“weightless?”“weightless?”


Satellites in OrbitSatellites in Orbit


Orbiting satellites are in free fall but Orbiting satellites are in free fall but miss the earth because it curves.miss the earth because it curves.

Summary Summary • The net force on a body executing circular The net force on a body executing circular motion is equal to the mass times the centripetal motion is equal to the mass times the centripetal acceleration of the body.acceleration of the body.

•aacentripedalcentripedal = = v v 22/ R/ R [toward the center] [toward the center]

• The “centrifugal” force is a fictitious force due to The “centrifugal” force is a fictitious force due to a non-inertial frame of reference.a non-inertial frame of reference.


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Physics 1710 Chapter 6—Circular Motion