In [1]:

```
import math #Example 7_1
#To convert angles to radians and revolutions
theta=70.0 #units in degrees
deg=360.0 #units in degrees
rad=theta*2*math.pi/deg #units in radians
rev=1 #units in revolution
rev=theta*rev/deg #units in revolution
print " 70 degrees in radians is ",round(rad,2),"radians \n 70 degrees in revolutions it is ",round(rev,3)," revolutions"
```

In [2]:

```
import math #Example 7_2
#To find average angular velocity
theta=1800.0 #units in rev
t=60.0 #units in sec
w=(theta/t) #units in rev/sec
w=w*(2*math.pi) #units in rad/sec
print "Average angular velocity is w=",round(w)," rad/sec"
```

In [3]:

```
import math #Example 7_3
#To find average angular acceleration
wf=240.0 #units in rev/sec
w0=0 #units in rev/sec
t=2.0 #units in minutes
t=t*60 #units in sec
alpha=(wf-w0)/t #units in rev/sec**2
print "Average angular acceleration is alpha=",round(alpha)," rev/sec**2"
```

In [4]:

```
import math #Example 7_4
#To find out how many revolutions does it turn before rest
wf=0 #units in rev/sec
w0=3 #units in rev/sec
t=18 #units in sec
alpha=(wf-w0)/t #units in rev/sec**2
theta=(w0*t)+0.5*(alpha*t**2) #units in rev
print "Number of revolutions does it turn before rest is theta=",round(theta)," rev"
```

In [5]:

```
import math #Example 7_5
#To find the angular acceleration and angular velocity of one wheel
vtf=20.0 #units in meters/sec
r=0.4 #units in meters
wf=vtf/r #units in rad/sec
vf=20.0 #units in meters/sec
v0=0 #units in meters/sec**2
t=9.0 #units in sec
a=(vf-v0)/t #units in meters/sec**2
alpha=a/r #units in rad/sec**2
print "Angular accelertion is a=",round(a,2)," meters/sec**2\n"
print "Angular velocity is alpha=",round(alpha,2)," rad/sec**2"
```

In [6]:

```
import math #Example 7_6
#To find out the rotation rate
at=8.6 #units in meters/sec**2
r=0.2 #units in meters
alpha=at/r #units in rad/sec**2
t=3 #units in sec
wf=alpha*t #units in rad/sec
print "The rotation rate is wf=",round(wf)," rad/sec"
```

In [7]:

```
import math #Example 7_7
#To calculate how large a horizontal force must the pavement exert
m=1200.0 #units in Kg
v=8.0 #units in meters/sec
r=9 #units in meters
F=(m*v**2)/r #units in Newtons
print "The horizontal force must the pavement exerts is F=",round(F)," Newtons"
#In text book the answer is printed wrong as F=8530 N but the correct answer is 8533 N
```

In [8]:

```
import math #Example 7_9
#To find out the angle where it should be banked
v=25 #units in meters/sec
r=60 #units in meters
g=9.8 #units in meters/sec**2
tantheta=v**2/(r*g) #units in radians
theta=math.atan(tantheta)*180/math.pi
print "The angle where it should be banked is theta=",round(theta)," degrees",
```

In [9]:

```
import math #Example 7_10
#To find out the ratio of F/W
G=6.67*10**-11 #units in Newton meter**2/Kg**2
m1=0.0080 #units in Kgs
m2=0.0080 #units in Kgs
r=2 #units in Meters
F=(G*m1*m2)/r**2 #units in Newtons
m=m1 #units in Kgs
g=9.8 #units in meter/sec**2
W=m*g #units in Newtons
F_W=F/W
print "The F/W Ratio is=",round(F_W,16)
```

In [10]:

```
import math #Example 7_11
#To find the mass of the sun
t=3.15*10**7 #units in sec
r=1.5*10**11 #units in meters
v=(2*math.pi*r)/t #units in meters/sec
G=6.67*10**-11 #units in Newtons
ms=(v**2*r)/G #Units in Kg
print "The mass of the sun is Ms=",round(ms,-28),"Kg"
```

In [11]:

```
import math #Example 7_12
#To findout the orbital radius and its speed
G=6.67*10**-11 #units in Newtons
me=5.98*10**24 #units in Kg
t=86400.0 #units in sec
r=((G*me*t**2)/(4*math.pi**2))**(1/3.0)
print "The orbital radius is r= ",round(r)," meters\n"
v=(2*math.pi*r)/t #units in meters/sec
print "The orbital speed is v=",round(v)," meters/sec"
#in textbook the answer is printed wrong as v=3070 m/sec but the correct answer is v=3073 m/sec
```