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{
"metadata": {
"name": "",
"signature": "sha256:b7bd6954751643f92d25f5c6d00ec1b3a41e28e3d14c6105ad117f2707f6395b"
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 4 Rotational motion of Rigid objects"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.1 Page no 54"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"w=4 #Angular velocity in rad/s\n",
"m=(1,2,3,4) #Masses in kg from the figure 4.17 on page no.54 \n",
"r=(2.5,1.5) #Centre position in m\n",
"\n",
"#Calculations\n",
"I=(m[0]+m[1]+m[2]+m[3])*(r[0]**2+r[1]**2)\n",
"KE=(1/2.0)*I*w**2\n",
"\n",
"#Output\n",
"print\"The moment of inertia is \",I,\"kg.m**2\" \n",
"print\"Kinetic energy of the system is \",KE,\"J\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The moment of inertia is 85.0 kg.m**2\n",
"Kinetic energy of the system is 680.0 J\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.2 Page no 55"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"q=30 #Angle of inclination in degrees\n",
"h=1 #Height in m\n",
"\n",
"#Calculations\n",
"import math\n",
"v=math.sqrt((10/7.0)*9.8*h)\n",
"a=(5/7.0)*9.8*math.sin(q*3.14/180.0)\n",
"\n",
"#Output\n",
"print\"Velocity and acceleration of the centre of mass of the sphere is \",round(v,2),\"m/s and \",round(a,1),\"m/s**2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity and acceleration of the centre of mass of the sphere is 3.74 m/s and 3.5 m/s**2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.3 Page no 55"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=1.2 #Mass of the rod in kg\n",
"l=0.8 #Length of the rod in m\n",
"\n",
"#Calculations\n",
"import math\n",
"T=2*3.14*math.sqrt((2*l)/(3.0*9.8))\n",
"\n",
"#Output\n",
"print\"Period of oscillation is \",round(T,2),\"s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Period of oscillation is 1.47 s\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.4 Page no 55"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"r=0.2 #Radius of uniform disc in m\n",
"d=0.15 #Distance from the centre in m\n",
"\n",
"#Calculations\n",
"import math\n",
"T=2*3.14*math.sqrt((17*r)/(12.0*9.8))\n",
"\n",
"#Output\n",
"print\"The period of oscillation is \",round(T,3),\"s\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The period of oscillation is 1.068 s\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.5 Page no 55"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"m=3 #Mass of the rotor in kg\n",
"I=0.03 #Moment of inertia in kg.m^2\n",
"d=0.25 #Distance of pivot from the centre in m\n",
"p=30 #Precession in rpm\n",
"\n",
"#Calculations\n",
"T=m*9.8*d\n",
"w=(p*2*3.14)/60.0\n",
"w1=(T/(I*w))\n",
"\n",
"#Output\n",
"print\"Angular speed of rotation of the rotor is \",round(w1,0),\"rpm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Angular speed of rotation of the rotor is 78.0 rpm\n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}
|
