W 7.8 FE/EIT: Circular motion graphs. (Section 8.3.2 and Hw 7.6). The following figure shows a NASA centrifuge that rotates a rigid arm A with a constant angular speed a relative to Earth (frame N). An astronaut (modeled as a particle Q) is rigidly strapped into the arm and moves at constant speed in a circle whose center N, is fixed in N. Radius of circle R = 10 m A's angular speed in N w = 2rad = rad 2 sec Form expressions and graph the quantities below. Form a. w. (measures of A's angu- lar acceleration, angular velocity, and angle, respectively). · 41 1.3 1.6 14 0 1 OF 04 82 0 = 2 1 a = = rad sec 05 1 05 1.5 1=8= 1 15 2 25 9 05 1 15 2 3 rad sec 7.9 Particle acopl 3 3.5 4 (radians). Use 0(t=0) = 0. 4 2.5 3 3.5 4 Forma, V, F (magnitudes of Q's acceleration and velocity in N and Q's position from N). Hint: Hw 7.6. 15 10 3 0 25 D 15 10 5 0 0 30 25 15 10 5 0 9 03 a = 0.5 1 0.5 V T 13 1 2 time (seconds) = F = R = 1.5 2 time (seconds) 2.5 15 2 2.5 m m S 3 3.5 meters 4 2.5 3 3.5 4 25 20 Form , , r (where r is the horizontally-right measure of magni- tudes of Q's position from No.). 15 10 Ï I= 3 0 -5 10 -15 -20 -25 0 16 12 4 -8 -12 -16 10 i 0 6 -6 -10 0.5 0.5 T= 0 0 0.5 1 1 1.5 1 Top view V 1.3 2 time (seconds) 25 1.3 R 2.5 2 time (seconds) 3 2 time (seconds) 25 3 3.5 (meters) 33 3 35 4 4
W 7.8 FE/EIT: Circular motion graphs. (Section 8.3.2 and Hw 7.6). The following figure shows a NASA centrifuge that rotates a rigid arm A with a constant angular speed a relative to Earth (frame N). An astronaut (modeled as a particle Q) is rigidly strapped into the arm and moves at constant speed in a circle whose center N, is fixed in N. Radius of circle R = 10 m A's angular speed in N w = 2rad = rad 2 sec Form expressions and graph the quantities below. Form a. w. (measures of A's angu- lar acceleration, angular velocity, and angle, respectively). · 41 1.3 1.6 14 0 1 OF 04 82 0 = 2 1 a = = rad sec 05 1 05 1.5 1=8= 1 15 2 25 9 05 1 15 2 3 rad sec 7.9 Particle acopl 3 3.5 4 (radians). Use 0(t=0) = 0. 4 2.5 3 3.5 4 Forma, V, F (magnitudes of Q's acceleration and velocity in N and Q's position from N). Hint: Hw 7.6. 15 10 3 0 25 D 15 10 5 0 0 30 25 15 10 5 0 9 03 a = 0.5 1 0.5 V T 13 1 2 time (seconds) = F = R = 1.5 2 time (seconds) 2.5 15 2 2.5 m m S 3 3.5 meters 4 2.5 3 3.5 4 25 20 Form , , r (where r is the horizontally-right measure of magni- tudes of Q's position from No.). 15 10 Ï I= 3 0 -5 10 -15 -20 -25 0 16 12 4 -8 -12 -16 10 i 0 6 -6 -10 0.5 0.5 T= 0 0 0.5 1 1 1.5 1 Top view V 1.3 2 time (seconds) 25 1.3 R 2.5 2 time (seconds) 3 2 time (seconds) 25 3 3.5 (meters) 33 3 35 4 4
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Question
Transcribed Image Text:W²=0
7.8 FE/EIT: Circular motion graphs. (Section 8.3.2 and Hw 7.6).
The following figure shows a NASA centrifuge that rotates a rigid arm A with a constant angular
Top view
An astronaut (modeled as a particle Q) is rigidly
strapped into the arm and moves at constant
speed in a circle whose center N, is fixed in N.
Radius of circle
R = 10 m
A's angular speed in N
W = 2 rad
4 sec
Form expressions and graph the quantities below.
1
Form a, w, e (measures of A's angu-
Forma, V, F (magnitudes of Q's
lar acceleration, angular velocity, and acceleration and velocity in N and Q's
position from No). Hint: Hw 7.6.
angle, respectively).
a = =
플
(.
0.6
0.4
0
18
1.6
12
1
0.8
0.6
0.4
0.2
0 6 =
6
5
2
0
0.5
1
W=
05
15
2
time (seconds)
0 =
rad
sec2
15 2 25
0.5 1 15 2
3
rad
sec
3
3.5
3.5
4
4
(radians). Use 0(t=0) = 0.
=
2 25 3 3.5 4
30
25
20
15
3
0
D
30
25
rad
2 sec
20
15
10
5
0
30
0
25
20
15
10
5
0
0
0.3
a
0.5
ŕ
0.5
1
V
1
1.5
1
2
time (seconds)
=
1.5
2.5
= R =
2.5
time (seconds)
3
m
S
1.5 2
time (seconds)
3.5
3
Can
4
3.5 4
meters
2.5 3 3.5
4
Form , , x (where is the
x
tudes of Q's position from N.).
horizontally-right measure of magni-
25
20
15
10
I
5
0
-5
-10
-15
-20
-25
0
16
12
8
-4
-12
0
10
8
6
7.9 Particle accelerator (with classical mechanics) (Section 8.3.1).
A particle moves along a curve (fixed to Earth) with velocity v = UT
and acceleration a = a + app, where 7 is tangent to the curve and
p is perpendicular. Determine the distances and elapsed time ty for
a particle to go from rest to 3y 106 m 11
Result
X =
-6
-10
0.5
x =
0
1
0.5
1.5
0.5 1 1.5
1
2
time (seconds)
2.5
2
time (seconds)
R
100
1.5 2
time (seconds)
3
3
3.5
1422
3.3
3
2.5
4
(meters)
3.5
A particle with a = 300 gs
takes 37 trips around
Earth's equator to reach
speed of light.
4
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