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PHYSICS 231 INTRODUCTORY PHYSICS I. Lecture 12. Last Lecture. Newton’s Law of gravitation Kepler’s Laws of Planetary motion Ellipses with sun at focus Sweep out equal areas in equal times. Gravitational Potential Energy. PE = mgh valid only near Earth’s surface For arbitrary altitude
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PHYSICS 231INTRODUCTORY PHYSICS I
Lecture 12
You wish to hurl a projectile from the surface of the Earth (Re= 6.38x106 m) to an altitude of 20x106 m above the surface of the Earth. Ignore rotation of the Earth and air resistance.
a) What initial velocity is required?
b) What velocity would be required in order for the projectile to reach infinitely high? I.e., what is the escape velocity?
c) (skip) How does the escape velocity compare to the velocity required for a low earth orbit?
a) 9,736 m/s
b) 11,181 m/s
c) 7,906 m/s
Chapter 8
Rotational Equilibrium
and
Rotational Dynamics
Door Demo
r
r
F
F
+

Φ is the angle between F and r
Given M = 120 kg.
Neglect the mass of the beam.
a) Find the tensionin the cable
b) What is the force
between the beam andthe wall
a) T=824 N b) f=353 N
Given: W=50 N, L=0.35 m, x=0.03 m
Find the tension in the muscle
W
x
L
F = 583 N
Given: x = 1.5 m, L = 5.0 m, wbeam = 300 N,
wman = 600 N
Find: T
T = 413 N
x
L
Consider the 400kgbeam shown below.Find TR
TR = 1 121 N
Given:
Wbeam=300
Wbox=200
Find:
Tleft
A
B
C
D
What point should I use for torque origin?
Given:
Tleft=300
Tright=500
Find:
Wbeam
A
B
C
D
What point should I use for torque origin?
Given:
Tleft=250
Tright=400
Find:
Wbox
A
B
C
D
What point should I use for torque origin?
Given:
Wbeam=300
Wbox=200
Find:
Tright
A
B
C
D
What point should I use for torque origin?
Given:
Tleft=250
Wbeam=250
Find:
Wbox
A
B
C
D
What point should I use for torque origin?
F
m
R
Analogous to relation between F and a
Moment of Inertia
What is the moment of inertia of the following point masses arranged in a square?
a) about the xaxis?
b) about the yaxis?
c) about the zaxis?
a) 0.72 kgm2
b) 1.08 kgm2
c) 1.8 kgm2
bicycle rim
filled can of coke
baton
baseball bat
basketball
boulder
Treat the spindle as a solid cylinder.
a) What is the moment of Inertia of the spindle? (M=5.0 kg, R=0.6 m)
b) If the tension in the rope is 10 N, what is the angular acceleration of the wheel?
c) What is the acceleration of the bucket?
d) What is the mass of the bucket?
M
a) 0.9 kgm2 b) 6.67 rad/s2 c) 4 m/s2 d) 1.72 kg
A 600kg solid cylinder of radius 0.6 m which can rotate freely about its axis is accelerated
by hanging a 240 kg mass from the end by a string which is wrapped about the cylinder.a) Find the linear acceleration of the mass.
b) What is the speed of the mass after it has dropped 2.5 m?
4.36 m/s2
4.67 m/s