angular momentum ( l ) - units: angular momentum is a vector whose direction is perpendicular to the...
TRANSCRIPT
Angular Momentum (l) -
prl
vmrl
sinrmvl
Units:
m kgm smkgm
skgm2
Angular Momentum is a vector whose direction is perpendicular to the plane containing r and p given by the
right hand rule.
are whatorigin, the Aboutplane. the in lie vectors
three All. force aby upon acted is It
shown. as velocity and
vector position a has mass with particle A 1.
xy
NFF
smvv m.rr
kg.P
0.2
0.403
02
45
r
P.30
.30F
v
a. the angular momentum of the particle,
vmrl
sinrmvl
r
.30v
150 150sin0.40.20.3 smkgml
skgml
212 Out of the page
k̂
are whatorigin, the Aboutplane. the in lie vectors
three All. force aby upon acted is It
shown. as velocity and
vector position a has mass with particle A 1.
xy
NFF
smvv m.rr
kg.P
0.2
0.403
02
45
r
P.30
.30F
v
b. and the torque acting on the particle.
Fr
sinrF
r.30
.30sin0.20.3 Nm
Nm 0.3 Out of the page
k̂
F
2. Two objects are moving as shown. What is their total angular momentum about point O?
O
kg 5.6
kg 1.3
m 5.1
m 8.2s
m6.3
sm2.2
r
v
page the into is
since vmrl
v
r
page the of out is
since vmrl
12 llL
1
2
2. Two objects are moving as shown. What is their total angular momentum about point O?
O
kg 5.6
kg 1.3
m 5.1
m 8.2s
m6.3
sm2.2
12 llL
.90sin.90sin 111222 vmrvmrL
1
2
smkgms
mkgmL 2.25.65.16.31.38.2
skgmL
28.9 Out of the page
k̂
3. What is the angular momentum of a rigid object rotating about a fixed axis?
x
y
z
ir
iv
im
iiii vmrl
.90siniiii vmrl
iiii vmrl
n
iiii vmrL
1
Butii rv
n
iiii rmrL
1
3. What is the angular momentum of a rigid object rotating about a fixed axis?
L
x
y
z
n
iiii rmrL
1
Butim all for constant
n
iiirmL
1
2
But
n
iiirmI
1
2
IL Angular Momentum of a rigid object rotating about a fixed axis
ir
iv
im
3. Three particles, each of mass m, are fastened to each other and to a rotation axis by three massless strings, each with length l. The combination rotates around the rotational axis at O with angular velocity ω in such a way that the particles remain in a straight line. In terms of m, l and ω and relative to point O, what are
mm
m
ll
l
a. the rotational inertia of the combination,
3
1
2
iiirmI
222 32 lmlmmlI
222 94 mlmlmlI
214mlI
O
3. Three particles, each of mass m, are fastened to each other and to a rotation axis by three massless strings, each with length l. The combination rotates around the rotational axis at O with angular velocity ω in such a way that the particles remain in a straight line. In terms of m, l and ω and relative to point O, what are
mm
m
ll
l
b. the angular momentum of the middle particle,
2 methods
Treat as a separate object
vmrlm
sinrmvlm
90sin2 mvllm
lmvlm 2
But rv lv 2
llmlm 22
24mllm
O
3. Three particles, each of mass m, are fastened to each other and to a rotation axis by three massless strings, each with length l. The combination rotates around the rotational axis at O with angular velocity ω in such a way that the particles remain in a straight line. In terms of m, l and ω and relative to point O, what are
mm
m
ll
l
b. the angular momentum of the middle particle,
2 methods
Treat as a rigid object
But
24mllm
mm Il
24mlIm
O
3. Three particles, each of mass m, are fastened to each other and to a rotation axis by three massless strings, each with length l. The combination rotates around the rotational axis at O with angular velocity ω in such a way that the particles remain in a straight line. In terms of m, l and ω and relative to point O, what are
mm
m
ll
l
c. the total angular momentum of the three particles.
IL
214mlL
O