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8.01SC Classical Mechanics Introduction

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📋 محتوى الكورس 200 درس · 16 ساعة 44 دقيقة

1 8.01SC Classical Mechanics Introduction 2:15
2 0.1 Vectors vs. Scalars 1:07
3 0.2 Vector Operators 2:14
4 0.3 Coordinate Systems and Unit Vectors 1:04
5 0.4 Vectors - Magnitude and Direction 0:40
6 0.5 Vector Decomposition into components 1:38
7 0.6 Going Between Representations 1:36
8 1.0 Week 1 Introduction (8.01 Classical Mechanics) 2:15
9 1.1 Coordinate Systems and Unit Vectors in 1D 3:06
10 1.2 Position Vector in 1D 2:25
11 1.3 Displacement Vector in 1D 3:28
12 1.4 Average Velocity in 1D 2:18
13 1.5 Instantaneous Velocity in 1D 5:40
14 1.7 Worked Example: Derivatives in Kinematics 3:08
15 2.1 Introduction to Acceleration 3:26
16 2.2 Acceleration in 1D 4:29
17 2.3 Worked Example: Acceleration from Position 3:45
18 2.4 Integration 22:34
19 3.1 Coordinate System and Position Vector in 2D 2:17
20 3.2 Instantaneous Velocity in 2D 6:12
21 3.3 Instantaneous Acceleration in 2D 5:20
22 3.4 Projectile Motion 6:12
23 3.5 Demo: Shooting an Apple 0:52
24 3.5 Demo: Relative Motion Gun 0:35
25 PS.1.1 Three Questions Before Starting 2:07
26 PS.1.2 Shooting the apple solution 10:19
27 P.1.3 Worked Example: Braking Car 6:47
28 P.1.4 Sketch the Motion 2:10
29 P.1.5 Worked Example: Pedestrian and Bike at Intersection 13:59
30 4.0 Week 2 Introduction 2:23
31 4.1 Newton's First and Second Laws 4:16
32 4.2 Newton's Third Law 7:15
33 4.3 Reference Frames 9:26
34 4.4 Non-inertial Reference Frames 4:38
35 5.1 Universal Law of Gravitation 6:55
36 5.2 Worked Example: Gravity - Superposition 8:46
37 5.3 Gravity at the surface of the Earth: The value of g. 4:49
38 6.1 Contact Forces 3:18
39 6.2 Static Friction 3:20
40 7.1 Pushing Pulling and Tension 4:17
41 7.2 Ideal Rope 4:58
42 7.3 Solving Pulley Systems 9:56
43 7.4 Hooke's Law 6:00
44 DD.1.1 Friction at the Nanoscale 39:12
45 PS.2.1 Worked Example - Sliding Block 6:20
46 PS.2.2 Worked Example - Stacked Blocks - Free Body Diagrams and Applying Newtons 2nd Law 8:13
47 PS.2.2 Worked Example - Stacked Blocks - Solve for the Maximum Force 4:44
48 PS.2.2 Worked Example - Stacked Blocks - Choosing the System of 2 Blocks Together 5:28
49 PS.2.3 Window Washer Free Body Diagrams 10:13
50 PS.2.3 Window Washer Solution 2:26
51 Newton's 3rd Law Pairs 4:18
52 Internal and External Forces 3:44
53 Applying Newton's 2nd Law 3:17
54 8.0 Week 3 Introduction 1:27
55 8.1 Polar Coordinates 3:35
56 8.2 Circular Motion: Position and Velocity Vectors 6:02
57 8.3 Angular Velocity 5:31
58 9.1 Uniform Circular Motion 3:50
59 9.2 Uniform Circular Motion: Direction of the Acceleration 3:36
60 10.1 Circular Motion - Acceleration 4:00
61 10.2 Angular Acceleration 6:21
62 10.3 Worked Example - Angular position from angular acceleration. 4:45
63 11.1 Newton's 2nd Law and Circular Motion 3:17
64 11.2 Worked Example - Car on a Banked Turn 7:37
65 11.3 Demo: Rotating Bucket 0:40
66 PS.3.1 Worked Example - Orbital Circular Motion - Radius 3:44
67 PS.3.1 Worked Example - Orbital Circular Motion - Velocity 1:07
68 PS.3.1 Worked Example - Orbital Circular Motion - Period 1:40
69 12.0 Week 4 Introduction 2:16
70 12.1 Pulley Problems 10:30
71 12.2 Constraint Condition 7:07
72 12.3 Virtual Displacement 3:43
73 12.4 Solve the System of Equations 4:04
74 12.5 Worked Example: 2 Blocks and 2 Pulleys 8:41
75 13.1 Rope Hanging Between Trees 3:36
76 13.2 Differential Analysis of a Massive Rope 15:34
77 13.3 Differential Elements 1:04
78 13.4 Density 0:52
79 13.5 Demo: Wrapping Friction 1:01
80 13.6 Summary for Differential Analysis 1:18
81 14.1 Intro to resistive forces 4:52
82 14.2 Resistive forces - low speed case 8:26
83 14.3 Resistive forces - high speed case 10:50
84 15.0 Week 5 Introduction 2:28
85 15.1 Momentum and Impulse 7:21
86 15.2 Impulse is a Vector 3:16
87 15.3 Worked Example - Bouncing Ball 6:38
88 15.4 Momentum of a System of Point Particles 4:45
89 15.5 Force on a System of Particles 9:06
90 16.1 Cases of Constant Momentum 5:34
91 16.2 Momentum Diagrams 5:18
92 17.1 Definition of the Center of Mass 4:32
93 17.2 Worked Example - Center of Mass of 3 Objects 7:14
94 17.3 Center of Mass of a Continuous System 2:55
95 17.5 Worked Example - Center of Mass of a Uniform Rod 5:51
96 17.6 Velocity and Acceleration of the Center of Mass 4:16
97 17.7 Reduction of a System to a Point Particle 4:03
98 18.0 Week 6 Introduction 0:53
99 18.1 Relative Velocity 1:57
100 18.2 Set up a Recoil Problem 6:28
101 18.3 Solve for Velocity in the Ground Frame 3:00
102 18.4 Solve for Velocity in the Moving Frame 2:09
103 19.1 Rocket Problem 1 - Set up the Problem 3:48
104 19.2 Rocket Problem 2 - Momentum Diagrams 5:00
105 19.3 Rocket Problem 3 - Mass Relations 2:50
106 19.4 Rocket Problem 4 - Solution 5:30
107 19.5 Rocket Problem 5 - Thrust and External Forces 3:28
108 19.6 Rocket Problem 6 - Solution for No External Forces 5:10
109 19.7 Rocket Problem 7 - Solution with External Forces 5:07
110 PS.6.1 Rocket Sled - Differential Equation 3:11
111 PS.6.1 Rocket Sled - Integrate the Rocket Equation 3:33
112 PS.6.1 Rocket Sled - Solve for Initial Velocity 1:03
113 PS.6.2 Snowplow Problem 8:11
114 20.0 Week 7 Introduction 2:04
115 20.1 Kinetic Energy 2:41
116 20.2 Work by a Constant Force 3:44
117 20.3 Work by a Non-Constant Force 6:20
118 20.4 Integrate adt and adx 4:50
119 20.5 Work-Kinetic Energy Theorem 1:56
120 20.6 Power 1:07
121 21.1 Scalar Product Properties 7:47
122 21.2 Scalar Product in Cartesian Coordinates 4:50
123 21.3 Kinetic Energy as a Scalar Product 2:01
124 21.4 Work in 2D and 3D 5:25
125 21.5 Work-Kinetic Energy Theorem in 2D and 3D 5:51
126 21.6 Worked Example: Block Going Down a Ramp 5:59
127 22.1 Path Independence - Gravity 5:39
128 22.2 Path Dependence - Friction 5:17
129 22.3 Conservative Forces 2:30
130 22.4 Non-conservative Forces 1:44
131 22.5 Summary of Work and Kinetic Energy 7:00
132 PS.7.1 Worked Example - Collision and Sliding on a Rough Surface 6:47
133 23.0 Week 8 Introduction 0:55
134 23.1 Introduction to Potential Energy 9:51
135 23.2 Potential Energy of Gravity near the Surface of the Earth 3:54
136 23.3 Potential Energy Reference State 5:01
137 23.4 Potential Energy of a Spring 5:20
138 23.5 Potential Energy of Gravitation 7:40
139 24.1 Mechanical Energy and Energy Conservation 5:56
140 24.2 Energy State Diagrams 5:34
141 24.3 Worked Example - Block Sliding Down Circular Slope 7:28
142 24.4 Newton's 2nd Law and Energy Conservation 5:28
143 25.1 Force is the Derivative of Potential 3:59
144 25.2 Stable and Unstable Equilibrium Points 7:22
145 25.3 Reading Potential Energy Diagrams 5:22
146 26.0 Week 9 Introduction 1:34
147 26.1 Momentum in Collisions 4:12
148 26.2 Kinetic Energy in Collisions 5:14
149 26.3 Totally Inelastic Collisions 4:47
150 27.1 Worked Example: Elastic 1D Collision 10:33
151 27.2 Relative Velocity in 1D 3:43
152 27.3 Kinetic Energy and Momentum Equation 7:09
153 27.4 Worked Example: Elastic 1D Collision Again 5:23
154 27.5 Worked Example: Gravitational Slingshot 4:45
155 27.6 2D Collisions 6:46
156 DD.2.1 Position in the CM Frame 4:33
157 DD.2.2 Relative Velocity is Independent of Reference Frame 3:43
158 DD.2.3 1D Elastic Collision Velocities in CM Frame 3:46
159 DD.2.4 Worked Example: 1D Elastic Collision in CM Frame 6:02
160 DD.2.5 Kinetic Energy in Different Reference Frames 6:06
161 DD.2.6 Kinetic Energy in the CM Frame 4:27
162 DD.2.7 Change in the Kinetic Energy 3:53
163 28.0 Week 10 Introduction 2:36
164 28.1 Rigid Bodies 3:01
165 28.2 Introduction to Translation and Rotation 2:39
166 28.3 Review of Angular Velocity and Acceleration 3:14
167 29.1 Kinetic Energy of Rotation 6:27
168 29.2 Moment of Inertia of a Rod 4:20
169 29.3 Moment of Inertia of a Disc 5:41
170 29.4 Parallel Axis Theorem 4:11
171 29.5 Deep Dive - Moment of Inertia of a Sphere 5:32
172 29.6 Deep Dive - Derivation of the Parallel Axis Theorem 5:38
173 30.1 Introduction to Torque and Rotational Dynamics 9:52
174 30.2 Cross Product 5:09
175 30.3 Cross Product in Cartesian Coordinates 7:55
176 30.4 Torque 2:04
177 30.5 Torque from Gravity 4:44
178 31.1 Relationship between Torque and Angular Acceleration 9:06
179 31.2 Internal Torques Cancel in Pairs 3:26
180 31.3 Worked Example - Find the Moment of Inertia of a Disc from a Falling Mass 7:20
181 31.4 Worked Example - Atwood Machine 11:02
182 31.5 Massive Pulley Problems 3:45
183 31.7 Worked Example - Two Blocks and a Pulley Using Energy 7:37
184 PS.10.1 Worked Example - Blocks with Friction and Massive Pulley 16:08
185 32.0 Week 11 Introduction 1:52
186 32.1 Angular Momentum for a Point Particle 2:39
187 32.2 Calculating Angular Momentum 3:08
188 32.3 Worked Example - Angular Momentum About Different Points 6:10
189 32.4 Angular Momentum of Circular Motion 3:27
190 33.1 Worked Example - Angular Momentum of 2 Rotating Point Particles 7:00
191 33.2 Angular Momentum of a Symmetric Object 4:11
192 33.4 If Momentum is Zero then Angular Momentum is Independent of Origin 5:42
193 33.5 Kinetic Energy of a Symmetric Object 2:34
194 34.1 Torque Causes Angular Momentum to Change - Point Particle 2:59
195 34.2 Torque Causes Angular Momentum to Change - System of Particles 3:56
196 34.3 Angular Impulse 3:42
197 34.4 Demo: Bicycle Wheel Demo 0:38
198 34.5 Worked Example - Particle Hits Pivoted Ring 8:13
199 35.0 Week 12 Introduction 1:35
200 35.1 Translation and Rotation of a Wheel 3:18

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8.01SC Classical Mechanics Introduction

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8.01SC Classical Mechanics Introduction

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0.1 Vectors vs. Scalars

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كورس MIT 8.01SC Classical Mechanics, Fall 2016

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📋 محتوى الكورس 200 درس · 16 ساعة 44 دقيقة

1 8.01SC Classical Mechanics Introduction 2:15
2 0.1 Vectors vs. Scalars 1:07
3 0.2 Vector Operators 2:14
4 0.3 Coordinate Systems and Unit Vectors 1:04
5 0.4 Vectors - Magnitude and Direction 0:40
6 0.5 Vector Decomposition into components 1:38
7 0.6 Going Between Representations 1:36
8 1.0 Week 1 Introduction (8.01 Classical Mechanics) 2:15
9 1.1 Coordinate Systems and Unit Vectors in 1D 3:06
10 1.2 Position Vector in 1D 2:25
11 1.3 Displacement Vector in 1D 3:28
12 1.4 Average Velocity in 1D 2:18
13 1.5 Instantaneous Velocity in 1D 5:40
14 1.7 Worked Example: Derivatives in Kinematics 3:08
15 2.1 Introduction to Acceleration 3:26
16 2.2 Acceleration in 1D 4:29
17 2.3 Worked Example: Acceleration from Position 3:45
18 2.4 Integration 22:34
19 3.1 Coordinate System and Position Vector in 2D 2:17
20 3.2 Instantaneous Velocity in 2D 6:12
21 3.3 Instantaneous Acceleration in 2D 5:20
22 3.4 Projectile Motion 6:12
23 3.5 Demo: Shooting an Apple 0:52
24 3.5 Demo: Relative Motion Gun 0:35
25 PS.1.1 Three Questions Before Starting 2:07
26 PS.1.2 Shooting the apple solution 10:19
27 P.1.3 Worked Example: Braking Car 6:47
28 P.1.4 Sketch the Motion 2:10
29 P.1.5 Worked Example: Pedestrian and Bike at Intersection 13:59
30 4.0 Week 2 Introduction 2:23
31 4.1 Newton's First and Second Laws 4:16
32 4.2 Newton's Third Law 7:15
33 4.3 Reference Frames 9:26
34 4.4 Non-inertial Reference Frames 4:38
35 5.1 Universal Law of Gravitation 6:55
36 5.2 Worked Example: Gravity - Superposition 8:46
37 5.3 Gravity at the surface of the Earth: The value of g. 4:49
38 6.1 Contact Forces 3:18
39 6.2 Static Friction 3:20
40 7.1 Pushing Pulling and Tension 4:17
41 7.2 Ideal Rope 4:58
42 7.3 Solving Pulley Systems 9:56
43 7.4 Hooke's Law 6:00
44 DD.1.1 Friction at the Nanoscale 39:12
45 PS.2.1 Worked Example - Sliding Block 6:20
46 PS.2.2 Worked Example - Stacked Blocks - Free Body Diagrams and Applying Newtons 2nd Law 8:13
47 PS.2.2 Worked Example - Stacked Blocks - Solve for the Maximum Force 4:44
48 PS.2.2 Worked Example - Stacked Blocks - Choosing the System of 2 Blocks Together 5:28
49 PS.2.3 Window Washer Free Body Diagrams 10:13
50 PS.2.3 Window Washer Solution 2:26
51 Newton's 3rd Law Pairs 4:18
52 Internal and External Forces 3:44
53 Applying Newton's 2nd Law 3:17
54 8.0 Week 3 Introduction 1:27
55 8.1 Polar Coordinates 3:35
56 8.2 Circular Motion: Position and Velocity Vectors 6:02
57 8.3 Angular Velocity 5:31
58 9.1 Uniform Circular Motion 3:50
59 9.2 Uniform Circular Motion: Direction of the Acceleration 3:36
60 10.1 Circular Motion - Acceleration 4:00
61 10.2 Angular Acceleration 6:21
62 10.3 Worked Example - Angular position from angular acceleration. 4:45
63 11.1 Newton's 2nd Law and Circular Motion 3:17
64 11.2 Worked Example - Car on a Banked Turn 7:37
65 11.3 Demo: Rotating Bucket 0:40
66 PS.3.1 Worked Example - Orbital Circular Motion - Radius 3:44
67 PS.3.1 Worked Example - Orbital Circular Motion - Velocity 1:07
68 PS.3.1 Worked Example - Orbital Circular Motion - Period 1:40
69 12.0 Week 4 Introduction 2:16
70 12.1 Pulley Problems 10:30
71 12.2 Constraint Condition 7:07
72 12.3 Virtual Displacement 3:43
73 12.4 Solve the System of Equations 4:04
74 12.5 Worked Example: 2 Blocks and 2 Pulleys 8:41
75 13.1 Rope Hanging Between Trees 3:36
76 13.2 Differential Analysis of a Massive Rope 15:34
77 13.3 Differential Elements 1:04
78 13.4 Density 0:52
79 13.5 Demo: Wrapping Friction 1:01
80 13.6 Summary for Differential Analysis 1:18
81 14.1 Intro to resistive forces 4:52
82 14.2 Resistive forces - low speed case 8:26
83 14.3 Resistive forces - high speed case 10:50
84 15.0 Week 5 Introduction 2:28
85 15.1 Momentum and Impulse 7:21
86 15.2 Impulse is a Vector 3:16
87 15.3 Worked Example - Bouncing Ball 6:38
88 15.4 Momentum of a System of Point Particles 4:45
89 15.5 Force on a System of Particles 9:06
90 16.1 Cases of Constant Momentum 5:34
91 16.2 Momentum Diagrams 5:18
92 17.1 Definition of the Center of Mass 4:32
93 17.2 Worked Example - Center of Mass of 3 Objects 7:14
94 17.3 Center of Mass of a Continuous System 2:55
95 17.5 Worked Example - Center of Mass of a Uniform Rod 5:51
96 17.6 Velocity and Acceleration of the Center of Mass 4:16
97 17.7 Reduction of a System to a Point Particle 4:03
98 18.0 Week 6 Introduction 0:53
99 18.1 Relative Velocity 1:57
100 18.2 Set up a Recoil Problem 6:28
101 18.3 Solve for Velocity in the Ground Frame 3:00
102 18.4 Solve for Velocity in the Moving Frame 2:09
103 19.1 Rocket Problem 1 - Set up the Problem 3:48
104 19.2 Rocket Problem 2 - Momentum Diagrams 5:00
105 19.3 Rocket Problem 3 - Mass Relations 2:50
106 19.4 Rocket Problem 4 - Solution 5:30
107 19.5 Rocket Problem 5 - Thrust and External Forces 3:28
108 19.6 Rocket Problem 6 - Solution for No External Forces 5:10
109 19.7 Rocket Problem 7 - Solution with External Forces 5:07
110 PS.6.1 Rocket Sled - Differential Equation 3:11
111 PS.6.1 Rocket Sled - Integrate the Rocket Equation 3:33
112 PS.6.1 Rocket Sled - Solve for Initial Velocity 1:03
113 PS.6.2 Snowplow Problem 8:11
114 20.0 Week 7 Introduction 2:04
115 20.1 Kinetic Energy 2:41
116 20.2 Work by a Constant Force 3:44
117 20.3 Work by a Non-Constant Force 6:20
118 20.4 Integrate adt and adx 4:50
119 20.5 Work-Kinetic Energy Theorem 1:56
120 20.6 Power 1:07
121 21.1 Scalar Product Properties 7:47
122 21.2 Scalar Product in Cartesian Coordinates 4:50
123 21.3 Kinetic Energy as a Scalar Product 2:01
124 21.4 Work in 2D and 3D 5:25
125 21.5 Work-Kinetic Energy Theorem in 2D and 3D 5:51
126 21.6 Worked Example: Block Going Down a Ramp 5:59
127 22.1 Path Independence - Gravity 5:39
128 22.2 Path Dependence - Friction 5:17
129 22.3 Conservative Forces 2:30
130 22.4 Non-conservative Forces 1:44
131 22.5 Summary of Work and Kinetic Energy 7:00
132 PS.7.1 Worked Example - Collision and Sliding on a Rough Surface 6:47
133 23.0 Week 8 Introduction 0:55
134 23.1 Introduction to Potential Energy 9:51
135 23.2 Potential Energy of Gravity near the Surface of the Earth 3:54
136 23.3 Potential Energy Reference State 5:01
137 23.4 Potential Energy of a Spring 5:20
138 23.5 Potential Energy of Gravitation 7:40
139 24.1 Mechanical Energy and Energy Conservation 5:56
140 24.2 Energy State Diagrams 5:34
141 24.3 Worked Example - Block Sliding Down Circular Slope 7:28
142 24.4 Newton's 2nd Law and Energy Conservation 5:28
143 25.1 Force is the Derivative of Potential 3:59
144 25.2 Stable and Unstable Equilibrium Points 7:22
145 25.3 Reading Potential Energy Diagrams 5:22
146 26.0 Week 9 Introduction 1:34
147 26.1 Momentum in Collisions 4:12
148 26.2 Kinetic Energy in Collisions 5:14
149 26.3 Totally Inelastic Collisions 4:47
150 27.1 Worked Example: Elastic 1D Collision 10:33
151 27.2 Relative Velocity in 1D 3:43
152 27.3 Kinetic Energy and Momentum Equation 7:09
153 27.4 Worked Example: Elastic 1D Collision Again 5:23
154 27.5 Worked Example: Gravitational Slingshot 4:45
155 27.6 2D Collisions 6:46
156 DD.2.1 Position in the CM Frame 4:33
157 DD.2.2 Relative Velocity is Independent of Reference Frame 3:43
158 DD.2.3 1D Elastic Collision Velocities in CM Frame 3:46
159 DD.2.4 Worked Example: 1D Elastic Collision in CM Frame 6:02
160 DD.2.5 Kinetic Energy in Different Reference Frames 6:06
161 DD.2.6 Kinetic Energy in the CM Frame 4:27
162 DD.2.7 Change in the Kinetic Energy 3:53
163 28.0 Week 10 Introduction 2:36
164 28.1 Rigid Bodies 3:01
165 28.2 Introduction to Translation and Rotation 2:39
166 28.3 Review of Angular Velocity and Acceleration 3:14
167 29.1 Kinetic Energy of Rotation 6:27
168 29.2 Moment of Inertia of a Rod 4:20
169 29.3 Moment of Inertia of a Disc 5:41
170 29.4 Parallel Axis Theorem 4:11
171 29.5 Deep Dive - Moment of Inertia of a Sphere 5:32
172 29.6 Deep Dive - Derivation of the Parallel Axis Theorem 5:38
173 30.1 Introduction to Torque and Rotational Dynamics 9:52
174 30.2 Cross Product 5:09
175 30.3 Cross Product in Cartesian Coordinates 7:55
176 30.4 Torque 2:04
177 30.5 Torque from Gravity 4:44
178 31.1 Relationship between Torque and Angular Acceleration 9:06
179 31.2 Internal Torques Cancel in Pairs 3:26
180 31.3 Worked Example - Find the Moment of Inertia of a Disc from a Falling Mass 7:20
181 31.4 Worked Example - Atwood Machine 11:02
182 31.5 Massive Pulley Problems 3:45
183 31.7 Worked Example - Two Blocks and a Pulley Using Energy 7:37
184 PS.10.1 Worked Example - Blocks with Friction and Massive Pulley 16:08
185 32.0 Week 11 Introduction 1:52
186 32.1 Angular Momentum for a Point Particle 2:39
187 32.2 Calculating Angular Momentum 3:08
188 32.3 Worked Example - Angular Momentum About Different Points 6:10
189 32.4 Angular Momentum of Circular Motion 3:27
190 33.1 Worked Example - Angular Momentum of 2 Rotating Point Particles 7:00
191 33.2 Angular Momentum of a Symmetric Object 4:11
192 33.4 If Momentum is Zero then Angular Momentum is Independent of Origin 5:42
193 33.5 Kinetic Energy of a Symmetric Object 2:34
194 34.1 Torque Causes Angular Momentum to Change - Point Particle 2:59
195 34.2 Torque Causes Angular Momentum to Change - System of Particles 3:56
196 34.3 Angular Impulse 3:42
197 34.4 Demo: Bicycle Wheel Demo 0:38
198 34.5 Worked Example - Particle Hits Pivoted Ring 8:13
199 35.0 Week 12 Introduction 1:35
200 35.1 Translation and Rotation of a Wheel 3:18

كورس MIT 8.01SC Classical Mechanics, Fall 2016

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