In [9]:

```
import math #Example 8_1
#To find the rotational kinetic energy
m=5.98*10**24 #units in Kg
r=6.37*10**6 #units in meters
I=(2.0/5)*m*r**2 #units in Kg meter**2
t=86400 #units in sec
w=(2*math.pi)/(t) #units in rad/sec
KE=0.5*(I*w**2) #units in joules
print "The rotational kinetic energy is KE="
print round(KE,-27)
print "Joules"
```

In [10]:

```
import math #Example 8_2
#To find the angular acceleration of the wheel
m=30 #units in Kg
k=0.25 #units in meters
I=m*k**2 #units in Kg meter**2
force=1.8 #units in Newtons
levelarm=0.40 #nits in meters
tou=force*levelarm #units in Newton meter
alpha=tou/I #units in rad/sec**2
print "Angular acceleration is alpha=",round(alpha,3)," rad/sec**2"
```

In [11]:

```
import math #Example 8_3
#To find out how long does it take to accelerate and how far does wheel turn in this time and the rotational kinetic energy
force=8 #units in Newtons
arm=0.25 #units in meters
tou=force*arm #units in Newton meter
m=80 #units in Kg
b=arm #units in meters
I=0.5*m*b**2 #units in Kg meter**2
alpha=tou/I #units in rad/sec**2
wf=4*math.pi #units in rad/sec
w0=0 #units in rad/sec
t=(wf-w0)/alpha #units in sec
print "The time taken is t=",round(t,1)," sec\n"
theta=0.5*(wf+w0)*t #units in radians
print "The wheel goes a distance of theta=",round(theta,1)," rad\n"
KE=0.5*I*wf**2 #units in Joules
print "The rotational kinetic energy is KE=",round(KE)," Joules"
```

In [12]:

```
import math #Example 8_4
#To find out the angular acceleration and the distance the object falls
f1=29.4 #units in Newtons
r1=0.75 #units in meters
m1=40 #units in Kgs
r2=0.6 #units in meters
m2=3 #units in Kgs
alpha=(f1*r1)/((m1*r2**2)+(m2*r1**2)) #units in rad/sec**2
print "The angular acceleration is alpha=",round(alpha,2)," rad/sec**2\n"
a=r1*alpha #units in meters/sec**2
t=10 #units in sec
y=0.5*a*t**2 #units in meters
print "The objects goes a distance of y=",round(y,1)," meters"
```

In [15]:

```
import math #Example 8_5
#To find the speed of the object
m=3 #units in Kg
g=9.8 #units in meters/sec**2
h=0.80 #units in meters
m1=3 #units in Kg
m2=14.4 #units in Kg
r=0.75 #units in meters
v=math.sqrt((m*g*h)/((0.5*m1)+((0.5*m2)/r**2)))
print "The object is moving at v=",round(v,2)," meters/sec"
```

In [16]:

```
import math #Example 8_8
#To find out how long does the sun take to complete one revolution
ra_rb=10.0**5
noofrev=1.0/25 #units in rev/day
wafter=(ra_rb)**2*(noofrev)
t=86400 #units in sec
time=t/wafter #units in sec
print "The sun would take for one revolution in time="
print time,"sec"
```

In [17]:

```
import math #Example 8_9
#To find out the rotational speed
m=0.3 #units in Kg
r=0.035 #units in meters
Iw=0.5*m*r**2 #units in Kg meter**2
Ibt=8*10**-4 #units in Kg meter**2
w0=2 #units in rev/sec
wf=(Ibt*w0)/(Ibt+Iw) #units in rev/sec
print "The rotational speed is Wf=",round(wf,2)," rev/sec"
```