1. Physics 1710 Chapter 6—Circular Motion
Answer:
a = ∆v/∆t
a = (112 m/s)/(2.5 sec) = m/s2
Thrust = force
F = ma = (1800. kg)(44.8 m/s 2 ) ~ 81 kN

2. Physics 1710 Chapter 6—Circular Motion
1′ Lecture:
The net force on a body executing circular motion is equal to the mass times the centripetal acceleration of the body. Fcentripetal = m acentripetal
acentripetal = v 2/ R [toward the center]; a = -ω2 r
In non-inertial frames of reference one may sense fictitious forces.
At terminal velocity the velocity-dependent resistive forces balance the accelerating forces so that no further acceleration occurs.

3. Physics 1710 Chapter 6—Circular Motion
Centripetal Acceleration: vx vy
x = r cos θ y = r sin θ
vx = (dr/dt) cos θ- r sin θ(d θ/dt) vy = (dr/dt) sin θ+r cos θ(d θ/dt) Let (dr/dt) = 0 vx = - r ω sin θ vy = +r ω cos θ
ax = dvx /dt= d(- r ω sin θ)/dt = r ω2cos θ- r ω sin θ(d ω/dt) ay = dvy /dt= d(r ω cos θ)/dt = -r ω2sin θ+ r ω cos θ(d ω/dt) a = - ω2 r + r (d vtangential /dt) θ

4. Physics 1710 Chapter 6—Circular Motion
Centripetal Acceleration: vx vy θ
a centripetal = - v 2 / r
a tangential = r (d vtangential /dt)
F = m a
F centripetal = m a centripetal = - mv 2 / r

5. Physics 1710 Chapter 6—Circular Motion
Demonstration: Ball on a String m v r
Fcentripetal
Fcentripetal = m v 2/r

6. Physics — e-Quiz
An athlete swings a 8 kg “hammer” around on a 1.2 m long cable at an angular frequency of 1.0 revolution per second. How much force must he exert on the hammer throw handle?
Answer Now !
About 12. N
About 30. N
About 78. N
About 380. 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

7. Physics 1710 Chapter 6—Circular Motion
Demonstration: Ball on a String m v r
Fcentripetal
v = 2π r/T = 2(3.14) (1.2 m)/(1.0 sec) = 7.5 m/s
Fcentripetal = m v 2/r = (8.0 kg)(7.5 m/s)2/(1.2 m)
= 378 N ~ 380 N

8. Physics 1710 Chapter 6—Circular Motion
Demonstration:
Marble in a bottle
Why does the marble stay up on the side?

9. Physics 1710 Chapter 6—Circular Motion
Why does the marble stay up on the side?
Think!
Confer!
No Talking!
Peer Instruction Time

10. Physics 1710 Chapter 6—Circular Motion
Satellites in Orbit
Which orbit is most like that of the Space Shuttle?

11. Physics 1710 Unit 1—Review 1 2 3 4 Think! Confer! No Talking!1 2 3 4
Think!
Confer!
No Talking!
Peer Instruction Time

12. Physics 1710 Chapter 6—Circular Motion
Satellite Motion:
h ~ 100 km , R⊕ ~ 6300 km
Fg= G Mm/ r 2 Gravity
Fg = Fr = mv 2/r
v = √[GM/r] = √[GM/(R⊕ + h)]~ √[GM/R⊕ ] = √[gR⊕ ]= √[(9.8 m/s2)(6.3 x106m) ]= 7.9x103 m/s ~17,600 mph
Why do the shuttle astronauts appear “weightless?”

13. Physics 1710 Chapter 6—Circular Motion
Satellites in Orbit
Orbiting satellites are in free fall but miss the earth because it curves.

14. Physics 1710 Chapter 6—Circular Motion
Summary
The net force on a body executing circular motion is equal to the mass times the centripetal acceleration of the body.
acentripedal = v 2/ R [toward the center]
The “centrifugal” force is a fictitious force due to a non-inertial frame of reference.