# Chapter8-Balancing of Rotating Masses¶

## Ex1-pg221¶

In :
##CHAPTER 8 ILLUSRTATION 1 PAGE NO 221
##TITLE:BALANCING OF ROTATING MASSES
pi=3.141
import math
mA=12.##       mass of A in kg
mB=10.##       mass of B in kg
mC=18.##       mass of C in kg
mD=15.##       mass of D in kg
rA=40.##       radius of A in mm
rB=50.##       radius of B in mm
rC=60.##       radius of C in mm
rD=30.##       radius of D in mm
theta1=0.##    angle between A-A in degrees
theta2=60.##   angle between A-B in degrees
theta3=130.##  angle between A-C in degrees
theta4=270.##  angle between A-D in degrees
R=100.##  radius at which mass to be determined in mm
##====================================================
Fh=(mA*rA*math.cos(theta1/57.3)+mB*rB*math.cos(theta2/57.3)+mC*rC*math.cos(theta3/57.3)+mD*rD*math.cos(theta4/57.3))/10.##    vertical component value in kg cm
Fv=(mA*rA*math.sin(theta1/57.3)+mB*rB*math.sin(theta2/57.3)+mC*rC*math.sin(theta3/57.3)+mD*rD*math.sin(theta4/57.3))/10.##   horizontal component value in kg cm
mb=(Fh**2.+Fv**2.)**.5/R*10.##     unbalanced mass in kg
theta=math.atan(Fv/Fh)*57.3##   position in degrees
THETA=180.+theta##       angle with mA
print'%s %.1f %s %.1f %s'%('magnitude of unbalaced mass=',mb,' kg'' angle with mA=',THETA,'degrees')

magnitude of unbalaced mass= 8.1  kg angle with mA= 267.5 degrees


## Ex2-pg222¶

In :
##CHAPTER 8 ILLUSRTATION 2 PAGE NO 222
##TITLE:BALANCING OF ROTATING MASSES
pi=3.141

mA=5.##   mass of A in kg
mB=10.##   mass of B in kg
mC=8.##     mass of C in kg
rA=10.##   radius of A in cm
rB=15.##   radius of B in cm
rC=10.##    radius of C in cm
rD=10.##   radius of D in cm
rE=15.##   radius of E in cm
##============================
mD=182./rD##    mass of D in kg by mearument
mE=80./rE##     mass of E in kg  by mearument
print'%s %.1f %s %.1f %s '%('mass of D= ',mD,' kg''mass of E= ',mE,' kg')

mass of D=  18.2  kgmass of E=  5.3  kg


## Ex3-pg223¶

In :
##CHAPTER 8 ILLUSRTATION 3 PAGE NO 223
##TITLE:BALANCING OF ROTATING MASSES
pi=3.141

mA=200.##       mass of A in kg
mB=300.##       mass of B in kg
mC=400.##       mass of C in kg
mD=200.##       mass of D in kg
rA=80.##       radius of A in mm
rB=70.##       radius of B in mm
rC=60.##       radius of C in mm
rD=80.##       radius of D in mm
rX=100.##      radius of X in mm
rY=100.##     radius of Y in mm
##=====================
mY=7.3/.04##    mass of Y in kg by mearurement
mX=35./.1##      mass of X in kg by mearurement
thetaX=146.##   in degrees by mesurement
print'%s %.1f %s %.1f %s %.1f %s'%('mass of X=',mX,' kg'' mass of Y=',mY,' kg''angle with mA=',thetaX,' degrees')


mass of X= 350.0  kg mass of Y= 182.5  kgangle with mA= 146.0  degrees


## Ex4-pg225¶

In :
##CHAPTER 8 ILLUSRTATION 4 PAGE NO 225
##TITLE:BALANCING OF ROTATING MASSES
pi=3.141

mB=30##       mass of B in kg
mC=50##       mass of C in kg
mD=40##       mass of D in kg
rA=18##       radius of A in cm
rB=24##       radius of B in cm
rC=12##       radius of C in cm
rD=15##       radius of D in cm
##=============================
mA=3.6/.18##         mass of A by measurement in kg
theta=124.##          angle with mass B in degrees by measurement in degrees
y=3.6/(.18*20)##     position of A from B
print'%s %.1f %s %.1f %s %.1f %s'%('mass of A=',mA,' kg'' angle with mass B=',theta,' degrees'' position of A from B=',y,' m towards right of plane B')

mass of A= 20.0  kg angle with mass B= 124.0  degrees position of A from B= 1.0  m towards right of plane B


## Ex5-pg226¶

In :
##CHAPTER 8 ILLUSRTATION 5 PAGE NO 226
##TITLE:BALANCING OF ROTATING MASSES
pi=3.141

mB=10.##       mass of B in kg
mC=5.##       mass of C in kg
mD=4.##       mass of D in kg
rA=10.##       radius of A in cm
rB=12.5##       radius of B in cm
rC=20.##       radius of C in cm
rD=15.##       radius of D in cm
##=====================================
mA=7.##      mass of A in kg by mesurement
BC=118.##     angle between B and C in degrees by mesurement
BA=203.5##   angle between B and A in degrees by mesurement
BD=260.##     angle between B and D in degrees by mesurement
print'%s %.1f %s %.1f %s %.1f %s %.1f %s '%('Mass of A=',mA,' kg'' angle between B and C=',BC,' degrees''angle between B and A= ',BA,' degrees'' angle between B and D=',BD,' degrees')

Mass of A= 7.0  kg angle between B and C= 118.0  degreesangle between B and A=  203.5  degrees angle between B and D= 260.0  degrees


## Ex6-pg228¶

In :
##CHAPTER 8 ILLUSRTATION 6 PAGE NO 228
##TITLE:BALANCING OF ROTATING MASSES
pi=3.141

mB=36.##       mass of B in kg
mC=25.##       mass of C in kg
rA=20.##       radius of A in cm
rB=15.##       radius of B in cm
rC=15.##       radius of C in cm
rD=20.##       radius of D in cm
##==================================
mA=3.9/.2##       mass of A in kg by measurement
mD=16.5##        mass of D in kg by measurement
theta=252.##      angular position of D from B by measurement in degrees
print'%s %.1f %s %.1f %s %.1f %s'%('Mass of A= ',mA,' kg'' Mass od D= ',mD,' kg''  Angular position of D from B= ',theta,' degrees')

Mass of A=  19.5  kg Mass od D=  16.5  kg  Angular position of D from B=  252.0  degrees


## Ex7-pg229¶

In :
##CHAPTER 8 ILLUSRTATION 7 PAGE NO 229
##TITLE:BALANCING OF ROTATING MASSES

pi=3.141
mA=48.##     mass of A in kg
mB=56.##       mass of B in kg
mC=20.##       mass of C in kg
rA=1.5##       radius of A in cm
rB=1.5##       radius of B in cm
rC=1.25##       radius of C in cm
N=300.##   speed in rpm
d=1.8##   distance between bearing in cm
##================================

angle between pulleys B&A= 164.0  degrees angle between pulleys B&C=   129.0  degrees angle between pulleys A&C=  67.0  degrees out of balance couple=   868.2  N load on each bearing=  482.3  N