15
4 2 5 1 0011 0010 1010 1101 0001 0100 1011 Chapter 7.2 Notes Angular Momentum
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42510011 0010 1010 1101 0001 0100 1011
Chapter 72 Notes
Angular Momentum
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular momentum tells us how difficult it is to stop a rotating object
4251
0011 0010 1010 1101 0001 0100 1011
bullEquation for angular momentum = Inertia x angular velocity
bullL = Iw
4251
0011 0010 1010 1101 0001 0100 1011
bull Objects of equal mass but different shapes have different inertia
4251
0011 0010 1010 1101 0001 0100 1011
bull Equations for Inertia range frombull Circular Orbit = I = 23mr2
bull Solid Cylinder = I = 12mr2
(Irsquoll tell you which equation to use)
4251
0011 0010 1010 1101 0001 0100 1011
bull A basketball has a mass of 005 kg The ball has a diameter of 8m and is a sphere so we use the equation I = 23 mr2 The angular speed of the ball is 30 rads What is the angular momentum
bull Radius = Diameter 2 = 8 m 2 = 4 mbull I=23mr2=23(05g)(4m)2 =0005 kgm2
bull L = Iw = (0005)(30) = 016 kgm2 s
4251
0011 0010 1010 1101 0001 0100 1011
bull Newtonrsquos 2nd law of motion with angular momentum ndash Equations = Torque = Angular momentum time
bull T = L t
4251
0011 0010 1010 1101 0001 0100 1011
bull An astronaut grabs a satellite to stop it from spinning The satellite mass is 900 kg and it is spinning at 1 rads The radius is 7 m The astronaut must hold the satellite of 5 seconds what torque is required to stop the spin To find the Inertia use I = frac12 mr2
bull T=Lt First find L (angular momentum)bull T = 2205 5 = 441
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular impulse (equation) = Torque x time
bull Since angular impulse = change in angular momentum (equation) = Tt = L
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular momentum tells us how difficult it is to stop a rotating object
4251
0011 0010 1010 1101 0001 0100 1011
bullEquation for angular momentum = Inertia x angular velocity
bullL = Iw
4251
0011 0010 1010 1101 0001 0100 1011
bull Objects of equal mass but different shapes have different inertia
4251
0011 0010 1010 1101 0001 0100 1011
bull Equations for Inertia range frombull Circular Orbit = I = 23mr2
bull Solid Cylinder = I = 12mr2
(Irsquoll tell you which equation to use)
4251
0011 0010 1010 1101 0001 0100 1011
bull A basketball has a mass of 005 kg The ball has a diameter of 8m and is a sphere so we use the equation I = 23 mr2 The angular speed of the ball is 30 rads What is the angular momentum
bull Radius = Diameter 2 = 8 m 2 = 4 mbull I=23mr2=23(05g)(4m)2 =0005 kgm2
bull L = Iw = (0005)(30) = 016 kgm2 s
4251
0011 0010 1010 1101 0001 0100 1011
bull Newtonrsquos 2nd law of motion with angular momentum ndash Equations = Torque = Angular momentum time
bull T = L t
4251
0011 0010 1010 1101 0001 0100 1011
bull An astronaut grabs a satellite to stop it from spinning The satellite mass is 900 kg and it is spinning at 1 rads The radius is 7 m The astronaut must hold the satellite of 5 seconds what torque is required to stop the spin To find the Inertia use I = frac12 mr2
bull T=Lt First find L (angular momentum)bull T = 2205 5 = 441
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular impulse (equation) = Torque x time
bull Since angular impulse = change in angular momentum (equation) = Tt = L
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bullEquation for angular momentum = Inertia x angular velocity
bullL = Iw
4251
0011 0010 1010 1101 0001 0100 1011
bull Objects of equal mass but different shapes have different inertia
4251
0011 0010 1010 1101 0001 0100 1011
bull Equations for Inertia range frombull Circular Orbit = I = 23mr2
bull Solid Cylinder = I = 12mr2
(Irsquoll tell you which equation to use)
4251
0011 0010 1010 1101 0001 0100 1011
bull A basketball has a mass of 005 kg The ball has a diameter of 8m and is a sphere so we use the equation I = 23 mr2 The angular speed of the ball is 30 rads What is the angular momentum
bull Radius = Diameter 2 = 8 m 2 = 4 mbull I=23mr2=23(05g)(4m)2 =0005 kgm2
bull L = Iw = (0005)(30) = 016 kgm2 s
4251
0011 0010 1010 1101 0001 0100 1011
bull Newtonrsquos 2nd law of motion with angular momentum ndash Equations = Torque = Angular momentum time
bull T = L t
4251
0011 0010 1010 1101 0001 0100 1011
bull An astronaut grabs a satellite to stop it from spinning The satellite mass is 900 kg and it is spinning at 1 rads The radius is 7 m The astronaut must hold the satellite of 5 seconds what torque is required to stop the spin To find the Inertia use I = frac12 mr2
bull T=Lt First find L (angular momentum)bull T = 2205 5 = 441
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular impulse (equation) = Torque x time
bull Since angular impulse = change in angular momentum (equation) = Tt = L
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull Objects of equal mass but different shapes have different inertia
4251
0011 0010 1010 1101 0001 0100 1011
bull Equations for Inertia range frombull Circular Orbit = I = 23mr2
bull Solid Cylinder = I = 12mr2
(Irsquoll tell you which equation to use)
4251
0011 0010 1010 1101 0001 0100 1011
bull A basketball has a mass of 005 kg The ball has a diameter of 8m and is a sphere so we use the equation I = 23 mr2 The angular speed of the ball is 30 rads What is the angular momentum
bull Radius = Diameter 2 = 8 m 2 = 4 mbull I=23mr2=23(05g)(4m)2 =0005 kgm2
bull L = Iw = (0005)(30) = 016 kgm2 s
4251
0011 0010 1010 1101 0001 0100 1011
bull Newtonrsquos 2nd law of motion with angular momentum ndash Equations = Torque = Angular momentum time
bull T = L t
4251
0011 0010 1010 1101 0001 0100 1011
bull An astronaut grabs a satellite to stop it from spinning The satellite mass is 900 kg and it is spinning at 1 rads The radius is 7 m The astronaut must hold the satellite of 5 seconds what torque is required to stop the spin To find the Inertia use I = frac12 mr2
bull T=Lt First find L (angular momentum)bull T = 2205 5 = 441
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular impulse (equation) = Torque x time
bull Since angular impulse = change in angular momentum (equation) = Tt = L
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull Equations for Inertia range frombull Circular Orbit = I = 23mr2
bull Solid Cylinder = I = 12mr2
(Irsquoll tell you which equation to use)
4251
0011 0010 1010 1101 0001 0100 1011
bull A basketball has a mass of 005 kg The ball has a diameter of 8m and is a sphere so we use the equation I = 23 mr2 The angular speed of the ball is 30 rads What is the angular momentum
bull Radius = Diameter 2 = 8 m 2 = 4 mbull I=23mr2=23(05g)(4m)2 =0005 kgm2
bull L = Iw = (0005)(30) = 016 kgm2 s
4251
0011 0010 1010 1101 0001 0100 1011
bull Newtonrsquos 2nd law of motion with angular momentum ndash Equations = Torque = Angular momentum time
bull T = L t
4251
0011 0010 1010 1101 0001 0100 1011
bull An astronaut grabs a satellite to stop it from spinning The satellite mass is 900 kg and it is spinning at 1 rads The radius is 7 m The astronaut must hold the satellite of 5 seconds what torque is required to stop the spin To find the Inertia use I = frac12 mr2
bull T=Lt First find L (angular momentum)bull T = 2205 5 = 441
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular impulse (equation) = Torque x time
bull Since angular impulse = change in angular momentum (equation) = Tt = L
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull A basketball has a mass of 005 kg The ball has a diameter of 8m and is a sphere so we use the equation I = 23 mr2 The angular speed of the ball is 30 rads What is the angular momentum
bull Radius = Diameter 2 = 8 m 2 = 4 mbull I=23mr2=23(05g)(4m)2 =0005 kgm2
bull L = Iw = (0005)(30) = 016 kgm2 s
4251
0011 0010 1010 1101 0001 0100 1011
bull Newtonrsquos 2nd law of motion with angular momentum ndash Equations = Torque = Angular momentum time
bull T = L t
4251
0011 0010 1010 1101 0001 0100 1011
bull An astronaut grabs a satellite to stop it from spinning The satellite mass is 900 kg and it is spinning at 1 rads The radius is 7 m The astronaut must hold the satellite of 5 seconds what torque is required to stop the spin To find the Inertia use I = frac12 mr2
bull T=Lt First find L (angular momentum)bull T = 2205 5 = 441
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular impulse (equation) = Torque x time
bull Since angular impulse = change in angular momentum (equation) = Tt = L
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull Newtonrsquos 2nd law of motion with angular momentum ndash Equations = Torque = Angular momentum time
bull T = L t
4251
0011 0010 1010 1101 0001 0100 1011
bull An astronaut grabs a satellite to stop it from spinning The satellite mass is 900 kg and it is spinning at 1 rads The radius is 7 m The astronaut must hold the satellite of 5 seconds what torque is required to stop the spin To find the Inertia use I = frac12 mr2
bull T=Lt First find L (angular momentum)bull T = 2205 5 = 441
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular impulse (equation) = Torque x time
bull Since angular impulse = change in angular momentum (equation) = Tt = L
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull An astronaut grabs a satellite to stop it from spinning The satellite mass is 900 kg and it is spinning at 1 rads The radius is 7 m The astronaut must hold the satellite of 5 seconds what torque is required to stop the spin To find the Inertia use I = frac12 mr2
bull T=Lt First find L (angular momentum)bull T = 2205 5 = 441
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular impulse (equation) = Torque x time
bull Since angular impulse = change in angular momentum (equation) = Tt = L
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull Angular impulse (equation) = Torque x time
bull Since angular impulse = change in angular momentum (equation) = Tt = L
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull A 100 kg potterrsquos wheel is 2 meters in radius What is the torque if the time is 10 seconds and the equation for I=12 mr2 and the angular speed of the wheel is 22 rads
bull Tt = L bull First find L (angular momentum)bull T(10) = 4400bull T = 4400 10 = 440
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull Law of conservation of angular momentum says that when no net external torque acts on a closed system the total angular momentum of the system does not change
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
42510011 0010 1010 1101 0001 0100 1011
Rotating Stool Demo
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bullLaw of conservation of angular momentum equation = L1 = L2
bullI1w1 = I2w2
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
4251
0011 0010 1010 1101 0001 0100 1011
bull If a skater starts with a moment of inertia of 5 with a speed of 2 than he brings in this arm to change his moment of inertia to 2 What happens to his speed
bull I1w1 = I2w2
bull 5(2) = 2(w2)bull 10 = 2w2
bull w2 = 5
