Chapter07: Motion in a Circle¶

Ex7.1:pg-208¶

In :
import math  #Example 7_1

#To convert angles to radians and revolutions
theta=70.0      #units in degrees
deg=360.0     #units in degrees
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"
70 degrees in revolutions it is  0.194  revolutions

Ex7.2:pg-209¶

In :
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
print "Average angular velocity is w=",round(w)," rad/sec"
Average angular velocity is w= 188.0  rad/sec

Ex7.3:pg-210¶

In :
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"
Average angular acceleration is alpha= 2.0  rev/sec**2

Ex7.4:pg-212¶

In :
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"
Number of revolutions does it turn before rest is theta= -108.0  rev

Ex7.5:pg-212¶

In :
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
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
print "Angular accelertion is a=",round(a,2)," meters/sec**2\n"
print "Angular velocity is alpha=",round(alpha,2)," rad/sec**2"
Angular accelertion is a= 2.22  meters/sec**2

Angular velocity is alpha= 5.56  rad/sec**2

Ex7.6:pg-213¶

In :
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
t=3     #units in sec
print "The rotation rate is wf=",round(wf)," rad/sec"
The rotation rate is wf= 129.0  rad/sec

Ex7.7:pg-215¶

In :
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
The horizontal force must the pavement exerts is F= 8533.0  Newtons

Ex7.9:pg-220¶

In :
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
theta=math.atan(tantheta)*180/math.pi
print "The angle where it should be banked is theta=",round(theta)," degrees",
The angle where it should be banked is theta= 47.0  degrees

Ex7.10:pg-220¶

In :
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)
The F/W Ratio is= 1.36e-14

Ex7.11:pg-221¶

In :
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"
The mass of the sun is Ms= 2.01e+30 Kg

Ex7.12:pg-222¶

In :
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
The orbital radius is r=  42250474.0  meters

The orbital speed is v= 3073.0  meters/sec