05physics_lecture_29 mar 2014
TRANSCRIPT
MS101: Physics
Chapter 5Dr. Ahmed Amin Hussein
May 3, 2023 Prepared By: Dr. Ahmed Amin 1
Chapter 5: Circular Motion
May 3, 2023 2Prepared By: Dr. Ahmed Amin
Uniform Circular Motion Radial Acceleration Banked and Unbanked Curves Circular Orbits Non-uniform Circular Motion Tangential and Angular
Acceleration Artificial Gravity
§5.1 Uniform Circular Motion
May 3, 2023 3Prepared By: Dr. Ahmed Amin
is the angular position.
Angular displacement:
if
Note: angles measured CW are negative and angles measured CCW are positive. is measured in radians.
2 radians = 360 = 1 revolution
x
y
i
f
May 3, 2023 4Prepared By: Dr. Ahmed Amin
The average and instantaneous angular velocities are:
tt t
0av lim and
is measured in rads/sec.
May 3, 2023 5Prepared By: Dr. Ahmed Amin
x
y
i
f
r
arclength = s = r
rs
is a ratio of two lengths; it is a dimensionless ratio!
May 3, 2023 6Prepared By: Dr. Ahmed Amin
An object moves along a circular path of radius r; what is its average speed?
avav timetotaldistance total r
tr
trv
Also, rv (instantaneous values).
x
y
i
f
r
May 3, 2023 7Prepared By: Dr. Ahmed Amin
The time it takes to go one time around a closed path is called the period (T).
Trv 2
timetotaldistance total
av
Comparing to v = r: fT
22
f is called the frequency, the number of revolutions (or cycles) per second.
§5.4 Circular Orbits
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rvmam
rMGmFF srs
esg
2
2
Consider an object of mass m in a circular orbit about the Earth.
Earth
r
The only force on the satellite is the force of gravity:
rGMv
rvm
rMGm
e
ses
2
2Solve for the speed of the satellite:
May 3, 2023 9Prepared By: Dr. Ahmed Amin
How high above the surface of the Earth does a satellite need to be so that it has an orbit period of 24 hours?
rGMv eFrom previous slide: Also need,
Trv 2
Combine these expressions and solve for r:3
12
24
TGMr e
m 10225.4
s 864004
kg 1098.5/kgNm1067.6
7
31
22
242211
r
km 000,35 ee RrhhRr
Example
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31
224
TGMr e
is Kepler’s Third Law.
It can be generalized to:3
1
224
TGMr
Where M is the mass of the central body. For example, it would be Msun if speaking of the planets in the solar system.
TMA Exercises
May 3, 2023 11Prepared By: Dr. Ahmed Amin
Problems :
Questions # # 5, 9, 13,
Additional questions
Questions # 31, 33, 35