Circular (Rotational) Motion Angular Speed and Angular Acceleration Centripetal (Radial)...
Transcript of Circular (Rotational) Motion Angular Speed and Angular Acceleration Centripetal (Radial)...
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Circular (Rotational) Motion
Angular Speed andAngular Acceleration
Centripetal (Radial) AccelerationRadial Forces
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Arc Length, s, and Angular Position, • s subtends angle at
___________ radius r• measured in _______
counterclockwise from x-axis
1.7r
s
Fig. 7.1, p. 191
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Angular Displacement
• Difference between final and initial angular positions
• Units are radians (rad)• Positive if
__________________
2.7if
Fig. 7.3, p. 191
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Angular Speed
• Divide angular displacement by time interval
• Units are _________
3.7av ttt if
if
Fig. 7.3, p. 191 4.7lim
0 tt
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Angular Acceleration
• Divide angular speed by time interval
• Units are _________
5.7av ttt if
if
Fig. 7.4, p. 193
6.7lim0 tt
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Angular Kinematics w/ = const
• Draw analogy with linear motion (a = const)
xavv
attvx
atvv
220
2
221
0
0 9.72
8.7
7.7
20
2
221
0
0
tt
tRotational MotionLinear Motion
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Relating Linear to Angular• _________ of v related to • Called _________ velocity vt
• Also have tangential accleration at
10.7rvt
Fig. 7.5, p. 196
11.7rat
All points have ______ angular speed & acceleration; points further from origin have ______ linear speed & acceleration
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Centripetal Acceleration
• v always _____________ to r• If Δt small then Δs and Δ small
• v points toward _______• Use similar triangles (a) and (b):
Fig. 7.7, p. 200
sr
vv
r
s
v
v
r
v
t
s
r
v
t
va
2
av
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Centripetal Acceleration
r
vac
2
rvt
17.72rac
Put it all together:
Total acceleration: 18.722ct aaa
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Centripetal Forces• Can be any of our familiar forces• Tension, friction, normal, gravitational
19.72
r
vmmaF cc
• Apply Newton’s 2nd Law to radial, tangential, and perpendicular directions
• Net centripetal force is:
rc FF
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Typical Applications
• Vehicle making a turn on an unbanked curve (friction only)
• Vehicle making a turn on a banked curve (no friction)
• The Gravitron amusement ride• Vertical circular motion
– Ferris Wheels– Loop-the-loops (roller coasters)