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"source": [
"# Chapter07: Motion in a Cirlce"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.1:pg-208"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 70 degrees in radians is 1.22 radians \n",
" 70 degrees in revolutions it is 0.194 revolutions\n"
]
}
],
"source": [
" import math #Example 7_1\n",
" \n",
" \n",
" #To convert angles to radians and revolutions\n",
"theta=70.0 #units in degrees\n",
"deg=360.0 #units in degrees\n",
"rad=theta*2*math.pi/deg #units in radians\n",
"rev=1 #units in revolution\n",
"rev=theta*rev/deg #units in revolution\n",
"print \" 70 degrees in radians is \",round(rad,2),\"radians \\n 70 degrees in revolutions it is \",round(rev,3),\" revolutions\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.2:pg-209"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average angular velocity is w= 188.0 rad/sec\n"
]
}
],
"source": [
" import math #Example 7_2\n",
" \n",
" \n",
"#To find average angular velocity\n",
"theta=1800.0 #units in rev\n",
"t=60.0 #units in sec\n",
"w=(theta/t) #units in rev/sec\n",
"w=w*(2*math.pi) #units in rad/sec\n",
"print \"Average angular velocity is w=\",round(w),\" rad/sec\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.3:pg-210"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Average angular acceleration is alpha= 2.0 rev/sec**2\n"
]
}
],
"source": [
" import math #Example 7_3\n",
" \n",
" \n",
" #To find average angular acceleration\n",
"wf=240.0 #units in rev/sec\n",
"w0=0 #units in rev/sec\n",
"t=2.0 #units in minutes\n",
"t=t*60 #units in sec\n",
"alpha=(wf-w0)/t #units in rev/sec**2\n",
"print \"Average angular acceleration is alpha=\",round(alpha),\" rev/sec**2\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.4:pg-212"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of revolutions does it turn before rest is theta= -108.0 rev\n"
]
}
],
"source": [
" import math #Example 7_4\n",
" \n",
" \n",
"#To find out how many revolutions does it turn before rest\n",
"wf=0 #units in rev/sec\n",
"w0=3 #units in rev/sec\n",
"t=18 #units in sec\n",
"alpha=(wf-w0)/t #units in rev/sec**2\n",
"theta=(w0*t)+0.5*(alpha*t**2) #units in rev\n",
"print \"Number of revolutions does it turn before rest is theta=\",round(theta),\" rev\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.5:pg-212"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Angular accelertion is a= 2.22 meters/sec**2\n",
"\n",
"Angular velocity is alpha= 5.56 rad/sec**2\n"
]
}
],
"source": [
" import math #Example 7_5\n",
" \n",
" \n",
" #To find the angular acceleration and angular velocity of one wheel\n",
"vtf=20.0 #units in meters/sec\n",
"r=0.4 #units in meters\n",
"wf=vtf/r #units in rad/sec\n",
"vf=20.0 #units in meters/sec\n",
"v0=0 #units in meters/sec**2\n",
"t=9.0 #units in sec\n",
"a=(vf-v0)/t #units in meters/sec**2\n",
"alpha=a/r #units in rad/sec**2\n",
"print \"Angular accelertion is a=\",round(a,2),\" meters/sec**2\\n\"\n",
"print \"Angular velocity is alpha=\",round(alpha,2),\" rad/sec**2\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.6:pg-213"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The rotation rate is wf= 129.0 rad/sec\n"
]
}
],
"source": [
" import math #Example 7_6\n",
" \n",
" \n",
" #To find out the rotation rate\n",
"at=8.6 #units in meters/sec**2\n",
"r=0.2 #units in meters\n",
"alpha=at/r #units in rad/sec**2\n",
"t=3 #units in sec\n",
"wf=alpha*t #units in rad/sec\n",
"print \"The rotation rate is wf=\",round(wf),\" rad/sec\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.7:pg-215"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The horizontal force must the pavement exerts is F= 8533.0 Newtons\n"
]
}
],
"source": [
" import math #Example 7_7\n",
" \n",
" \n",
" #To calculate how large a horizontal force must the pavement exert\n",
"m=1200.0 #units in Kg\n",
"v=8.0 #units in meters/sec\n",
"r=9 #units in meters\n",
"F=(m*v**2)/r #units in Newtons\n",
"print \"The horizontal force must the pavement exerts is F=\",round(F),\" Newtons\"\n",
" #In text book the answer is printed wrong as F=8530 N but the correct answer is 8533 N\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.9:pg-220"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The angle where it should be banked is theta= 47.0 degrees\n"
]
}
],
"source": [
" import math #Example 7_9\n",
" \n",
" \n",
" #To find out the angle where it should be banked\n",
"v=25 #units in meters/sec\n",
"r=60 #units in meters\n",
"g=9.8 #units in meters/sec**2\n",
"tantheta=v**2/(r*g) #units in radians\n",
"theta=math.atan(tantheta)*180/math.pi\n",
"print \"The angle where it should be banked is theta=\",round(theta),\" degrees\",\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.10:pg-220"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The F/W Ratio is= 1.36e-14\n"
]
}
],
"source": [
" import math #Example 7_10\n",
" \n",
" \n",
" #To find out the ratio of F/W\n",
"G=6.67*10**-11 #units in Newton meter**2/Kg**2\n",
"m1=0.0080 #units in Kgs\n",
"m2=0.0080 #units in Kgs\n",
"r=2 #units in Meters\n",
"F=(G*m1*m2)/r**2 #units in Newtons\n",
"m=m1 #units in Kgs\n",
"g=9.8 #units in meter/sec**2\n",
"W=m*g #units in Newtons\n",
"F_W=F/W\n",
"print \"The F/W Ratio is=\",round(F_W,16)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.11:pg-221"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mass of the sun is Ms= 2.01e+30 Kg\n"
]
}
],
"source": [
" import math #Example 7_11\n",
" \n",
" \n",
" #To find the mass of the sun\n",
"t=3.15*10**7 #units in sec\n",
"r=1.5*10**11 #units in meters\n",
"v=(2*math.pi*r)/t #units in meters/sec\n",
"G=6.67*10**-11 #units in Newtons\n",
"ms=(v**2*r)/G #Units in Kg\n",
"print \"The mass of the sun is Ms=\",round(ms,-28),\"Kg\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex7.12:pg-222"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The orbital radius is r= 42250474.0 meters\n",
"\n",
"The orbital speed is v= 3073.0 meters/sec\n"
]
}
],
"source": [
" import math #Example 7_12\n",
" \n",
" \n",
" #To findout the orbital radius and its speed\n",
"G=6.67*10**-11 #units in Newtons\n",
"me=5.98*10**24 #units in Kg\n",
"t=86400.0 #units in sec\n",
"r=((G*me*t**2)/(4*math.pi**2))**(1/3.0)\n",
"print \"The orbital radius is r= \",round(r),\" meters\\n\"\n",
"v=(2*math.pi*r)/t #units in meters/sec\n",
"print \"The orbital speed is v=\",round(v),\" meters/sec\"\n",
" #in textbook the answer is printed wrong as v=3070 m/sec but the correct answer is v=3073 m/sec\n"
]
}
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