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