copy 2010 Pearson Education Inc
copy 2010 Pearson Education Inc Slide 7-4
ldquoMomentrdquo comes from momentumhellip meaning motion
copy 2010 Pearson Education Inc
A net torque applied to an object
causeshellip
A a linear acceleration of the
object
B the object to rotate at a constant
rate
C the angular velocity of the object
to change
D the moment of inertia of the
object to change
Slide 7-11
copy 2010 Pearson Education Inc
Answer
A net torque applied to an object
causeshellip
A a linear acceleration of the object
B the object to rotate at a constant
rate
Cthe angular velocity of the
object to change
D the moment of inertia of the object
to change
Slide 7-12
copy 2010 Pearson Education Inc
Another questionhellip
Moment of inertia ishellip
A the rotational equivalent of mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-5
copy 2010 Pearson Education Inc
Answer
Moment of inertia ishellip
Athe rotational equivalent of
mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-6
copy 2010 Pearson Education Inc
Newtonrsquos Second Law for Rotation
a = t II = moment of inertia Objects with larger
moments of inertia are harder to get rotating
I = miri2aring
Slide 7-34
copy 2010 Pearson Education Inc
Recallhellip Net Torque (τnet) =
Angular Acceleration (α) Rotational Inertia (I)
α = τnetI
α = ΔωΔt
τnetI = ΔωΔt
τnet Δt = I Δω
Similar tohellip
Fnet Δt = m Δv = Δp
τnet Δt = I Δω = ΔL
Similarlyhellip
Net Torque acting for some time causes the angular momentum (L) to change
τnet Δt = I Δω = ΔL
copy 2010 Pearson Education Inc
Rotational Inertia (I) and Conservation of Angular Momentum (Lf = Li)
Why does the guy
above have a lot of
rotational inertia
Which TP has more
Inertia
Why
The diverrsquos rotational
momentum is
conserved Where is
angular velocity
(rotation rate)
greatest Why
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc Slide 7-4
ldquoMomentrdquo comes from momentumhellip meaning motion
copy 2010 Pearson Education Inc
A net torque applied to an object
causeshellip
A a linear acceleration of the
object
B the object to rotate at a constant
rate
C the angular velocity of the object
to change
D the moment of inertia of the
object to change
Slide 7-11
copy 2010 Pearson Education Inc
Answer
A net torque applied to an object
causeshellip
A a linear acceleration of the object
B the object to rotate at a constant
rate
Cthe angular velocity of the
object to change
D the moment of inertia of the object
to change
Slide 7-12
copy 2010 Pearson Education Inc
Another questionhellip
Moment of inertia ishellip
A the rotational equivalent of mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-5
copy 2010 Pearson Education Inc
Answer
Moment of inertia ishellip
Athe rotational equivalent of
mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-6
copy 2010 Pearson Education Inc
Newtonrsquos Second Law for Rotation
a = t II = moment of inertia Objects with larger
moments of inertia are harder to get rotating
I = miri2aring
Slide 7-34
copy 2010 Pearson Education Inc
Recallhellip Net Torque (τnet) =
Angular Acceleration (α) Rotational Inertia (I)
α = τnetI
α = ΔωΔt
τnetI = ΔωΔt
τnet Δt = I Δω
Similar tohellip
Fnet Δt = m Δv = Δp
τnet Δt = I Δω = ΔL
Similarlyhellip
Net Torque acting for some time causes the angular momentum (L) to change
τnet Δt = I Δω = ΔL
copy 2010 Pearson Education Inc
Rotational Inertia (I) and Conservation of Angular Momentum (Lf = Li)
Why does the guy
above have a lot of
rotational inertia
Which TP has more
Inertia
Why
The diverrsquos rotational
momentum is
conserved Where is
angular velocity
(rotation rate)
greatest Why
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
A net torque applied to an object
causeshellip
A a linear acceleration of the
object
B the object to rotate at a constant
rate
C the angular velocity of the object
to change
D the moment of inertia of the
object to change
Slide 7-11
copy 2010 Pearson Education Inc
Answer
A net torque applied to an object
causeshellip
A a linear acceleration of the object
B the object to rotate at a constant
rate
Cthe angular velocity of the
object to change
D the moment of inertia of the object
to change
Slide 7-12
copy 2010 Pearson Education Inc
Another questionhellip
Moment of inertia ishellip
A the rotational equivalent of mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-5
copy 2010 Pearson Education Inc
Answer
Moment of inertia ishellip
Athe rotational equivalent of
mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-6
copy 2010 Pearson Education Inc
Newtonrsquos Second Law for Rotation
a = t II = moment of inertia Objects with larger
moments of inertia are harder to get rotating
I = miri2aring
Slide 7-34
copy 2010 Pearson Education Inc
Recallhellip Net Torque (τnet) =
Angular Acceleration (α) Rotational Inertia (I)
α = τnetI
α = ΔωΔt
τnetI = ΔωΔt
τnet Δt = I Δω
Similar tohellip
Fnet Δt = m Δv = Δp
τnet Δt = I Δω = ΔL
Similarlyhellip
Net Torque acting for some time causes the angular momentum (L) to change
τnet Δt = I Δω = ΔL
copy 2010 Pearson Education Inc
Rotational Inertia (I) and Conservation of Angular Momentum (Lf = Li)
Why does the guy
above have a lot of
rotational inertia
Which TP has more
Inertia
Why
The diverrsquos rotational
momentum is
conserved Where is
angular velocity
(rotation rate)
greatest Why
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Answer
A net torque applied to an object
causeshellip
A a linear acceleration of the object
B the object to rotate at a constant
rate
Cthe angular velocity of the
object to change
D the moment of inertia of the object
to change
Slide 7-12
copy 2010 Pearson Education Inc
Another questionhellip
Moment of inertia ishellip
A the rotational equivalent of mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-5
copy 2010 Pearson Education Inc
Answer
Moment of inertia ishellip
Athe rotational equivalent of
mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-6
copy 2010 Pearson Education Inc
Newtonrsquos Second Law for Rotation
a = t II = moment of inertia Objects with larger
moments of inertia are harder to get rotating
I = miri2aring
Slide 7-34
copy 2010 Pearson Education Inc
Recallhellip Net Torque (τnet) =
Angular Acceleration (α) Rotational Inertia (I)
α = τnetI
α = ΔωΔt
τnetI = ΔωΔt
τnet Δt = I Δω
Similar tohellip
Fnet Δt = m Δv = Δp
τnet Δt = I Δω = ΔL
Similarlyhellip
Net Torque acting for some time causes the angular momentum (L) to change
τnet Δt = I Δω = ΔL
copy 2010 Pearson Education Inc
Rotational Inertia (I) and Conservation of Angular Momentum (Lf = Li)
Why does the guy
above have a lot of
rotational inertia
Which TP has more
Inertia
Why
The diverrsquos rotational
momentum is
conserved Where is
angular velocity
(rotation rate)
greatest Why
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Another questionhellip
Moment of inertia ishellip
A the rotational equivalent of mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-5
copy 2010 Pearson Education Inc
Answer
Moment of inertia ishellip
Athe rotational equivalent of
mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-6
copy 2010 Pearson Education Inc
Newtonrsquos Second Law for Rotation
a = t II = moment of inertia Objects with larger
moments of inertia are harder to get rotating
I = miri2aring
Slide 7-34
copy 2010 Pearson Education Inc
Recallhellip Net Torque (τnet) =
Angular Acceleration (α) Rotational Inertia (I)
α = τnetI
α = ΔωΔt
τnetI = ΔωΔt
τnet Δt = I Δω
Similar tohellip
Fnet Δt = m Δv = Δp
τnet Δt = I Δω = ΔL
Similarlyhellip
Net Torque acting for some time causes the angular momentum (L) to change
τnet Δt = I Δω = ΔL
copy 2010 Pearson Education Inc
Rotational Inertia (I) and Conservation of Angular Momentum (Lf = Li)
Why does the guy
above have a lot of
rotational inertia
Which TP has more
Inertia
Why
The diverrsquos rotational
momentum is
conserved Where is
angular velocity
(rotation rate)
greatest Why
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Answer
Moment of inertia ishellip
Athe rotational equivalent of
mass
B the point at which all forces appear
to act
C the time at which inertia occurs
D an alternative term for moment arm
Slide 7-6
copy 2010 Pearson Education Inc
Newtonrsquos Second Law for Rotation
a = t II = moment of inertia Objects with larger
moments of inertia are harder to get rotating
I = miri2aring
Slide 7-34
copy 2010 Pearson Education Inc
Recallhellip Net Torque (τnet) =
Angular Acceleration (α) Rotational Inertia (I)
α = τnetI
α = ΔωΔt
τnetI = ΔωΔt
τnet Δt = I Δω
Similar tohellip
Fnet Δt = m Δv = Δp
τnet Δt = I Δω = ΔL
Similarlyhellip
Net Torque acting for some time causes the angular momentum (L) to change
τnet Δt = I Δω = ΔL
copy 2010 Pearson Education Inc
Rotational Inertia (I) and Conservation of Angular Momentum (Lf = Li)
Why does the guy
above have a lot of
rotational inertia
Which TP has more
Inertia
Why
The diverrsquos rotational
momentum is
conserved Where is
angular velocity
(rotation rate)
greatest Why
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Newtonrsquos Second Law for Rotation
a = t II = moment of inertia Objects with larger
moments of inertia are harder to get rotating
I = miri2aring
Slide 7-34
copy 2010 Pearson Education Inc
Recallhellip Net Torque (τnet) =
Angular Acceleration (α) Rotational Inertia (I)
α = τnetI
α = ΔωΔt
τnetI = ΔωΔt
τnet Δt = I Δω
Similar tohellip
Fnet Δt = m Δv = Δp
τnet Δt = I Δω = ΔL
Similarlyhellip
Net Torque acting for some time causes the angular momentum (L) to change
τnet Δt = I Δω = ΔL
copy 2010 Pearson Education Inc
Rotational Inertia (I) and Conservation of Angular Momentum (Lf = Li)
Why does the guy
above have a lot of
rotational inertia
Which TP has more
Inertia
Why
The diverrsquos rotational
momentum is
conserved Where is
angular velocity
(rotation rate)
greatest Why
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Recallhellip Net Torque (τnet) =
Angular Acceleration (α) Rotational Inertia (I)
α = τnetI
α = ΔωΔt
τnetI = ΔωΔt
τnet Δt = I Δω
Similar tohellip
Fnet Δt = m Δv = Δp
τnet Δt = I Δω = ΔL
Similarlyhellip
Net Torque acting for some time causes the angular momentum (L) to change
τnet Δt = I Δω = ΔL
copy 2010 Pearson Education Inc
Rotational Inertia (I) and Conservation of Angular Momentum (Lf = Li)
Why does the guy
above have a lot of
rotational inertia
Which TP has more
Inertia
Why
The diverrsquos rotational
momentum is
conserved Where is
angular velocity
(rotation rate)
greatest Why
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Rotational Inertia (I) and Conservation of Angular Momentum (Lf = Li)
Why does the guy
above have a lot of
rotational inertia
Which TP has more
Inertia
Why
The diverrsquos rotational
momentum is
conserved Where is
angular velocity
(rotation rate)
greatest Why
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Conservation of Angular Momentum (Lf = Li)
The angular momentum of a rotating object subject to no external net torque (τnet = 0) is a constant
The final angular momentum Lf is equal to the initial angular momentum Li
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Rotational Inertia (I) amp Angular Momentum (L = I ω) (Ch 9)
Angular Momentum is conserved
Linitial = Lfinal
Ii ωi = If ωf
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Moments of Inertia of Common Shapes
Slide 7-35
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
copy 2010 Pearson Education Inc
Angular Momentum = L = I ωLinear Momentum = p =mv
L = I ω
L = (mr2) ω
And ω = vr
L = mr2 ω = mr2 vr
L = m r v
L = m v r = p r
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