Topic 1: Angular Momentum Physics with Calculus I
p=mv linear momentum mass and motion
Torque=Force * Lever arm
Angular momentum is mass and rotation; motion
T=deltaL/deltaT
L=IW
T*deltat=deltaL
net force acting on an object =ma
Work=deltaRKE
net torque acting on an object =I* angular acceleration
dlineardisplacemnent=theta*R
Angular acceleration=change in angular;ar velocity =w/t
W=T*angular displacement
nrt torqure =I* deltaw/deltaT
1rev=2pirad
F=deltap/deltat
P=W/t
theta=angular displacement
Conservation of Momentum
P=T*angular velocity
Po=Pf us deltaF=0 Conservation of momentum
RKE=1/2Iw^2
Inelastic collisions combined
v=w*R
Conservation of Angular momentum and same nal speed
power rate of energ being
Lo=Lf if deltaT=0 elastic (different )
transferred
IoWo=IfWf L=m(r(vector)*v(vector)
vt=dr/dt
,Topic 1: Angular Momentum Physics with Calculus I Inertia Equati
, Guided Warm up: Angular Momentum Physics with Calculus I
3. A force of 300N acts on a 2.5m long rod initially at rest as shown in the picture below. (a) What is the torque acting on the rod? (
1
of the rod if the force acts on it for 8 seconds? (c) What is the nal angular speed of the rod? (d) How much work was done by the for
T=F*R=750 (a),
T=deltaL/delta
T=T*deltaT=Lf-Lo,
Lo0 rod initially at rest
Lf=T*deltaT=(750)(8)=6000 (b),
Lf=IWf, I=1/3mL^2(for a rod) =20.83WF=Lf=288(c)
W=deltaRKE=RKEf-0, Lf=IWf(d) W=RKEf=IWf^2
A 500kg merry-go-round with a radius of 10m is moving at a speed of 0.5 rad/s. A 40kg child jumps on the merry-go-round at a po
2
What is the inertia of the merry-go-round? (b) What is the inertia of the child on the merry-go-round? (c) What is the nal speed of
Inelastic collision Momentum Ic=mR^2=m(4)^2
I(c)w(c)+I(m)w(m)=I(c+m)w
, Homework Problems +Work and Answer: Angular Momentum Physics with Calculus I
1 A 2.00-kg mass is located at r= 2.00 im + 3.00 jm and has velocity = 4.00 im/s - 1.00 jm/s . What is the angular momentu
L=Iw
A × B = (A_x·B_y − A_y·B_x) k̂
L=m(r(vector)*v(vector)
-2-12=-14k*2=-28k
A 2.00-kg sphere is rotating about an axis through its center at 40.0 rev/s with the angular velocity in the +z direction. A torque 1
2
sphere in the +x direction. What is the rate of change of the angular momentum of the sphere?
T=dL/dt=10
A 40.0-kg child running at a speed 3.00 m/s jumps on a stationary playground merry-go-round at a distance 1.50 m from the axis
2
3 is traveling tangential to the edge of the merry-go-round which has a 600 kg·m moment of inertia about its axis of rotation as she i
merry-go-round after the child jumps on it?
mvr+0=I(c+m)Wf
p=mv linear momentum mass and motion
Torque=Force * Lever arm
Angular momentum is mass and rotation; motion
T=deltaL/deltaT
L=IW
T*deltat=deltaL
net force acting on an object =ma
Work=deltaRKE
net torque acting on an object =I* angular acceleration
dlineardisplacemnent=theta*R
Angular acceleration=change in angular;ar velocity =w/t
W=T*angular displacement
nrt torqure =I* deltaw/deltaT
1rev=2pirad
F=deltap/deltat
P=W/t
theta=angular displacement
Conservation of Momentum
P=T*angular velocity
Po=Pf us deltaF=0 Conservation of momentum
RKE=1/2Iw^2
Inelastic collisions combined
v=w*R
Conservation of Angular momentum and same nal speed
power rate of energ being
Lo=Lf if deltaT=0 elastic (different )
transferred
IoWo=IfWf L=m(r(vector)*v(vector)
vt=dr/dt
,Topic 1: Angular Momentum Physics with Calculus I Inertia Equati
, Guided Warm up: Angular Momentum Physics with Calculus I
3. A force of 300N acts on a 2.5m long rod initially at rest as shown in the picture below. (a) What is the torque acting on the rod? (
1
of the rod if the force acts on it for 8 seconds? (c) What is the nal angular speed of the rod? (d) How much work was done by the for
T=F*R=750 (a),
T=deltaL/delta
T=T*deltaT=Lf-Lo,
Lo0 rod initially at rest
Lf=T*deltaT=(750)(8)=6000 (b),
Lf=IWf, I=1/3mL^2(for a rod) =20.83WF=Lf=288(c)
W=deltaRKE=RKEf-0, Lf=IWf(d) W=RKEf=IWf^2
A 500kg merry-go-round with a radius of 10m is moving at a speed of 0.5 rad/s. A 40kg child jumps on the merry-go-round at a po
2
What is the inertia of the merry-go-round? (b) What is the inertia of the child on the merry-go-round? (c) What is the nal speed of
Inelastic collision Momentum Ic=mR^2=m(4)^2
I(c)w(c)+I(m)w(m)=I(c+m)w
, Homework Problems +Work and Answer: Angular Momentum Physics with Calculus I
1 A 2.00-kg mass is located at r= 2.00 im + 3.00 jm and has velocity = 4.00 im/s - 1.00 jm/s . What is the angular momentu
L=Iw
A × B = (A_x·B_y − A_y·B_x) k̂
L=m(r(vector)*v(vector)
-2-12=-14k*2=-28k
A 2.00-kg sphere is rotating about an axis through its center at 40.0 rev/s with the angular velocity in the +z direction. A torque 1
2
sphere in the +x direction. What is the rate of change of the angular momentum of the sphere?
T=dL/dt=10
A 40.0-kg child running at a speed 3.00 m/s jumps on a stationary playground merry-go-round at a distance 1.50 m from the axis
2
3 is traveling tangential to the edge of the merry-go-round which has a 600 kg·m moment of inertia about its axis of rotation as she i
merry-go-round after the child jumps on it?
mvr+0=I(c+m)Wf
