Chapter 08: Rotational work energy and momentum

Ex8.1:pg-240

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"

The rotational kinetic energy is KE=
2.57e+29
Joules

Ex8.2:pg-242

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"

Angular acceleration is alpha= 0.384  rad/sec**2

Ex8.3:pg-242

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"

The time taken is t= 15.7  sec

The wheel goes a distance of theta= 98.7  rad

The rotational kinetic energy is KE= 197.0  Joules

Ex8.4:pg-243

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"

The angular acceleration is alpha= 1.37  rad/sec**2

The objects goes a distance of y= 51.4  meters

Ex8.5:pg-244

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"

The object is moving at v= 1.28  meters/sec

Ex8.8:pg-247

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"

The sun would take for one revolution in time=
0.000216 sec

Ex8.9:pg-248

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"

The rotational speed is Wf= 1.63  rev/sec