1
00:00:00,000 --> 00:00:00,690


2
00:00:00,690 --> 00:00:03,010
Where I left off in the last
video we saw that if we had a

3
00:00:03,010 --> 00:00:06,610
magnetic field coming in from
the right and we had this loop

4
00:00:06,610 --> 00:00:10,900
of-- I guess we call it-- metal
or a circuit, and it's

5
00:00:10,900 --> 00:00:13,760
carrying a current where the
current is coming in this

6
00:00:13,760 --> 00:00:14,300
direction--.

7
00:00:14,300 --> 00:00:16,560
You can imagine positive
protons, although we know the

8
00:00:16,560 --> 00:00:17,810
electrons go in the
other direction.

9
00:00:17,810 --> 00:00:20,400
But the current is coming in
this direction and going out

10
00:00:20,400 --> 00:00:20,990
that direction.

11
00:00:20,990 --> 00:00:24,210
We figured out using the right
hand rule and just this

12
00:00:24,210 --> 00:00:27,890
formula, that the net force of
the magnetic field coming in

13
00:00:27,890 --> 00:00:31,850
this direction on this arm
of the wire or the

14
00:00:31,850 --> 00:00:34,520
circuit is net downwards.

15
00:00:34,520 --> 00:00:36,510
And on this arm, it
was net upwards.

16
00:00:36,510 --> 00:00:39,750
And so it provided a net
torque on this circuit.

17
00:00:39,750 --> 00:00:41,620
Or, as I said in the last
video, a paper clip.

18
00:00:41,620 --> 00:00:44,530
And where this dotted line
is the axis of rotation.

19
00:00:44,530 --> 00:00:46,610
And this is how I showed
you it would rotate.

20
00:00:46,610 --> 00:00:49,700
Where the magnetic field is
essentially pushing up on the

21
00:00:49,700 --> 00:00:51,840
right hand side and pushing down
on the left hand side.

22
00:00:51,840 --> 00:00:54,570
It has no effect over here on
the top and the bottom.

23
00:00:54,570 --> 00:00:58,230
So it would rotate in
this direction.

24
00:00:58,230 --> 00:01:01,610
And then this was kind of what
it looks like after it rotates

25
00:01:01,610 --> 00:01:02,040
a little bit.

26
00:01:02,040 --> 00:01:06,190
And the whole reason why I did
this, I said, well, this arm--

27
00:01:06,190 --> 00:01:08,130
which is the same as
this arm-- the net

28
00:01:08,130 --> 00:01:09,700
force is still upwards.

29
00:01:09,700 --> 00:01:11,160
Out of our screen.

30
00:01:11,160 --> 00:01:14,630
But that upwards direction is
now no longer going to be

31
00:01:14,630 --> 00:01:19,010
completely perpendicular to
the moment arm distance.

32
00:01:19,010 --> 00:01:20,770
That's the moment
arm distance.

33
00:01:20,770 --> 00:01:23,090
Now the moment arm distance is
kind of coming at an angle out

34
00:01:23,090 --> 00:01:23,940
of the page.

35
00:01:23,940 --> 00:01:27,540
So only some of this net outward
force for the magnetic

36
00:01:27,540 --> 00:01:30,600
field is going to
be perpendicular

37
00:01:30,600 --> 00:01:31,630
to the moment arm.

38
00:01:31,630 --> 00:01:34,300
And so the torque on it will be
less, but it's still going

39
00:01:34,300 --> 00:01:36,600
to be torque in that
same direction.

40
00:01:36,600 --> 00:01:39,090
Kind of coming out of the page
on the right and into the page

41
00:01:39,090 --> 00:01:39,580
on the left.

42
00:01:39,580 --> 00:01:41,330
And the same is true of
the left hand side.

43
00:01:41,330 --> 00:01:44,130
And you go all the way to the
point that the coil is

44
00:01:44,130 --> 00:01:45,560
actually vertical.

45
00:01:45,560 --> 00:01:49,580
Where this side, this side
right here, is on top.

46
00:01:49,580 --> 00:01:53,170
And this side is on bottom,
below the plane

47
00:01:53,170 --> 00:01:53,950
of your video screen.

48
00:01:53,950 --> 00:01:59,320
And at that point, the torque--
actually, there is no

49
00:01:59,320 --> 00:01:59,890
net torque.

50
00:01:59,890 --> 00:02:00,540
And why is that?

51
00:02:00,540 --> 00:02:03,810
Because on this top part, when
it's pointing straight out at

52
00:02:03,810 --> 00:02:09,060
you, when it's right here, the
magnetic field-- the force of

53
00:02:09,060 --> 00:02:13,270
it, the force that's affecting
the circuit-- is pushing

54
00:02:13,270 --> 00:02:14,160
straight up.

55
00:02:14,160 --> 00:02:17,080
So there's no longer any net
torque because the force is

56
00:02:17,080 --> 00:02:19,720
pushing straight up and that
moment arm distance-- this

57
00:02:19,720 --> 00:02:22,460
distance-- is now also
pointing straight up.

58
00:02:22,460 --> 00:02:25,700
And torque is also a cross
product, so you actually care

59
00:02:25,700 --> 00:02:28,080
about the perpendicular
forces.

60
00:02:28,080 --> 00:02:30,890
So there, at this vertical
point, there's no net torque.

61
00:02:30,890 --> 00:02:33,340
And the same is true at the
bottom of the circuit.

62
00:02:33,340 --> 00:02:36,160
Because at the bottom the
magnetic field force is going

63
00:02:36,160 --> 00:02:38,940
to be downwards, which is
parallel with the moment arm

64
00:02:38,940 --> 00:02:40,630
distance, so there's
no net torque.

65
00:02:40,630 --> 00:02:45,240
And I said, well maybe there's
a little bit of angular

66
00:02:45,240 --> 00:02:49,590
momentum that keeps this
object rotating.

67
00:02:49,590 --> 00:02:52,590
And then it will rotate to--
and this is where it gets

68
00:02:52,590 --> 00:02:53,360
interesting.

69
00:02:53,360 --> 00:02:55,810
I'll draw it neatly.

70
00:02:55,810 --> 00:02:58,900
Then it'll rotate
to this point.

71
00:02:58,900 --> 00:03:00,340
Once again I want to have
the perspective.

72
00:03:00,340 --> 00:03:08,666


73
00:03:08,666 --> 00:03:10,200
It'll rotate here.

74
00:03:10,200 --> 00:03:12,820
So let me just make sure
I have all of it.

75
00:03:12,820 --> 00:03:14,980
So here it was rotating in this

76
00:03:14,980 --> 00:03:20,060
direction and in that direction.

77
00:03:20,060 --> 00:03:22,860
And then here maybe some--
there's no longer any torque

78
00:03:22,860 --> 00:03:26,070
on it, but it still might on the
top be moving to the left,

79
00:03:26,070 --> 00:03:28,420
and on the bottom moving
to the right.

80
00:03:28,420 --> 00:03:31,230
Up to a point, then it's going
to get into this configuration

81
00:03:31,230 --> 00:03:38,160
where soon. this side is-- so
at this point it has rotated

82
00:03:38,160 --> 00:03:40,310
more than 90 degrees.

83
00:03:40,310 --> 00:03:42,970
So this edge is now this edge.

84
00:03:42,970 --> 00:03:46,110
It had rotated from here all the
way-- it's still pointing

85
00:03:46,110 --> 00:03:47,440
out of the screen.

86
00:03:47,440 --> 00:03:51,130
But if this edge is the same as
this edge, now the current

87
00:03:51,130 --> 00:03:53,080
direction is going
to be like this.

88
00:03:53,080 --> 00:03:56,180
Because this edge has
rotated down.

89
00:03:56,180 --> 00:03:59,440
So it's rotated from that
position all the way back to

90
00:03:59,440 --> 00:04:00,390
this position.

91
00:04:00,390 --> 00:04:02,920
So the current is now coming--
let me make sure, let me draw

92
00:04:02,920 --> 00:04:04,040
that right.

93
00:04:04,040 --> 00:04:08,050
The current is coming like that,
like that, like that.

94
00:04:08,050 --> 00:04:13,220
Going up here, to the
right, up like that.

95
00:04:13,220 --> 00:04:15,610
So the current now on this left
hand side, although it

96
00:04:15,610 --> 00:04:17,125
was the former right
hand side.

97
00:04:17,125 --> 00:04:20,380
It's still going in that
upwards direction.

98
00:04:20,380 --> 00:04:22,800
So when you take the cross
product, what is going to be

99
00:04:22,800 --> 00:04:25,230
the net magnetic
field on that?

100
00:04:25,230 --> 00:04:27,660
Or the force of the
magnetic field?

101
00:04:27,660 --> 00:04:31,050
Well, you do the same
right hand rule.

102
00:04:31,050 --> 00:04:32,730
Point your index finger up.

103
00:04:32,730 --> 00:04:34,170
Put your middle finger
in the direction of

104
00:04:34,170 --> 00:04:35,680
the magnetic field.

105
00:04:35,680 --> 00:04:38,120
This is the palm, this is
your other two fingers.

106
00:04:38,120 --> 00:04:40,300
Let me draw the fingernails,
just so they're painted

107
00:04:40,300 --> 00:04:40,890
fingernails.

108
00:04:40,890 --> 00:04:42,460
Not that mine are.

109
00:04:42,460 --> 00:04:44,620
Then your thumb points
upwards.

110
00:04:44,620 --> 00:04:51,370
So on this side of the coil we
still have an upwards force.

111
00:04:51,370 --> 00:04:53,350
And if you do the cross product,
or you do the right

112
00:04:53,350 --> 00:04:56,790
hand rule on the bottom side,
or the behind side, if you

113
00:04:56,790 --> 00:04:59,450
could imagine it, you're
still going to have a

114
00:04:59,450 --> 00:05:00,730
net downward force.

115
00:05:00,730 --> 00:05:02,470
So now all of a sudden
you could imagine--

116
00:05:02,470 --> 00:05:04,580
the thing had rotated.

117
00:05:04,580 --> 00:05:09,020
So it had rotated in the way I
drew it here, where it pops

118
00:05:09,020 --> 00:05:12,100
out on this side and it
goes in on that side.

119
00:05:12,100 --> 00:05:14,760
And it had done it all the way
to the point where we had

120
00:05:14,760 --> 00:05:17,800
rotated more than 90 degrees,
but now all of a sudden the

121
00:05:17,800 --> 00:05:21,560
net force through the magnetic
field was going to reverse.

122
00:05:21,560 --> 00:05:24,610
Because the side that has a
current going upwards is now

123
00:05:24,610 --> 00:05:26,360
the left hand side.

124
00:05:26,360 --> 00:05:28,830
So now the force from the
magnetic field is out on this

125
00:05:28,830 --> 00:05:31,660
side and you're going
to want to rotate in

126
00:05:31,660 --> 00:05:34,160
the opposite direction.

127
00:05:34,160 --> 00:05:34,970
Hopefully that makes sense.

128
00:05:34,970 --> 00:05:35,850
Just think about what happens.

129
00:05:35,850 --> 00:05:38,380
Visualize this coil rotating.

130
00:05:38,380 --> 00:05:42,190
So what is essentially going to
happen is you're going to

131
00:05:42,190 --> 00:05:46,610
rotate like I did
here on the top.

132
00:05:46,610 --> 00:05:48,910
Maybe once you get to this level
you're going to have a

133
00:05:48,910 --> 00:05:52,100
little bit of angular momentum
that'll keep you rotating.

134
00:05:52,100 --> 00:05:55,020
Or rotational inertia that'll
keep you rotating until you're

135
00:05:55,020 --> 00:05:56,510
in something like this
configuration.

136
00:05:56,510 --> 00:06:00,220
Maybe you go all the way back
to this configuration, where

137
00:06:00,220 --> 00:06:04,580
it's essentially a complete
180 degree turn.

138
00:06:04,580 --> 00:06:08,260
And then since on this side
the current's going to be

139
00:06:08,260 --> 00:06:10,360
going up and on this side the
current's going down, because

140
00:06:10,360 --> 00:06:14,060
you've essentially flipped
this thing over, then the

141
00:06:14,060 --> 00:06:17,120
effect of the magnetic field is
going to say, well, upwards

142
00:06:17,120 --> 00:06:19,540
on the left, downwards
on the right.

143
00:06:19,540 --> 00:06:20,900
And so it's going to
turn the other way.

144
00:06:20,900 --> 00:06:23,920
So if you think about it, it's
going to keep oscillating.

145
00:06:23,920 --> 00:06:27,490
Let me draw it from-- well, I
don't want to draw it from

146
00:06:27,490 --> 00:06:28,830
that angle, because I don't
want to confuse you.

147
00:06:28,830 --> 00:06:30,630
So we have a problem.

148
00:06:30,630 --> 00:06:33,810
If we wanted to turn this into
some type of electric motor

149
00:06:33,810 --> 00:06:37,840
and keep it spinning, we would
either have to reverse the

150
00:06:37,840 --> 00:06:41,330
current once you get into this
configuration, or either turn

151
00:06:41,330 --> 00:06:42,380
off the magnetic field.

152
00:06:42,380 --> 00:06:46,630
Or maybe you could reverse the
magnetic field to get it going

153
00:06:46,630 --> 00:06:47,510
in the other direction.

154
00:06:47,510 --> 00:06:49,540
And actually you have another
problem, which is a slightly

155
00:06:49,540 --> 00:06:52,730
lesser problem, is if this was
a circuit and you just kept

156
00:06:52,730 --> 00:06:55,770
turning over and over the
circuit, the wires would get

157
00:06:55,770 --> 00:06:56,280
twisted here.

158
00:06:56,280 --> 00:06:58,430
So you couldn't do
it indefinitely.

159
00:06:58,430 --> 00:07:03,373
So the solution here is
something called a commutator.

160
00:07:03,373 --> 00:07:05,630
you So let me draw
a commutator.

161
00:07:05,630 --> 00:07:10,720


162
00:07:10,720 --> 00:07:19,250
I have the same circuit which
I've now drawn messier.

163
00:07:19,250 --> 00:07:23,140


164
00:07:23,140 --> 00:07:24,430
But it has these two leads.

165
00:07:24,430 --> 00:07:27,120


166
00:07:27,120 --> 00:07:29,210
It has these leads that
essentially curve.

167
00:07:29,210 --> 00:07:31,960
You could imagine them curving
out of the page.

168
00:07:31,960 --> 00:07:35,040
And then we have a circuit.

169
00:07:35,040 --> 00:07:36,720
You could imagine
leads here, too.

170
00:07:36,720 --> 00:07:41,030
And this round thing and this
thing are touching each other

171
00:07:41,030 --> 00:07:43,150
the whole time, so current
could pass through it.

172
00:07:43,150 --> 00:07:47,000


173
00:07:47,000 --> 00:07:50,800
Let me draw my battery.

174
00:07:50,800 --> 00:07:52,710
This is positive and
this is negative.

175
00:07:52,710 --> 00:07:55,140
So up here on the circuit the
current's always going to be

176
00:07:55,140 --> 00:07:56,440
flowing in this direction.

177
00:07:56,440 --> 00:07:58,600
It's always going to be flowing
in this direction,

178
00:07:58,600 --> 00:08:02,460
it's always going to be flowing
up and like this.

179
00:08:02,460 --> 00:08:04,150
Now when you're in this
configuration,

180
00:08:04,150 --> 00:08:05,720
what's going to happen?

181
00:08:05,720 --> 00:08:08,860
Well, the current is going
to flow down here.

182
00:08:08,860 --> 00:08:12,750
That's going to be I and
that's going to be I.

183
00:08:12,750 --> 00:08:15,720
And when you do your right hand
rule, we have the same

184
00:08:15,720 --> 00:08:16,320
magnetic field.

185
00:08:16,320 --> 00:08:19,280
I haven't changed the magnetic
field coming in from the left.

186
00:08:19,280 --> 00:08:21,890


187
00:08:21,890 --> 00:08:24,700
So just like we did before I
cleared the screen, you use

188
00:08:24,700 --> 00:08:26,590
the right hand rule and you'll
figure out, well, the net

189
00:08:26,590 --> 00:08:32,090
force from the magnetic field
is going to be upwards here

190
00:08:32,090 --> 00:08:34,429
and downwards here.

191
00:08:34,429 --> 00:08:36,250
And that's what's going to
create that net torque.

192
00:08:36,250 --> 00:08:39,429
And you're going to
rotate this part.

193
00:08:39,429 --> 00:08:41,220
So this part of this

194
00:08:41,220 --> 00:08:43,260
contraption is going to rotate.

195
00:08:43,260 --> 00:08:44,510
You could imagine maybe
there's like

196
00:08:44,510 --> 00:08:45,870
a little pole here.

197
00:08:45,870 --> 00:08:48,910
Maybe it's a nonconducting pole
so that none of the-- and

198
00:08:48,910 --> 00:08:50,940
it's connected to an
axle somewhere.

199
00:08:50,940 --> 00:08:53,980
So you can rotate along
that axis, right?

200
00:08:53,980 --> 00:08:55,895
So the force of the
magnetic field is

201
00:08:55,895 --> 00:08:56,430
going to create a torque.

202
00:08:56,430 --> 00:09:00,930
We're going to rotate up on this
side, up out of the page

203
00:09:00,930 --> 00:09:03,030
on that side, and into the
page on that side.

204
00:09:03,030 --> 00:09:07,530
And then behind the page and
then back out of the page.

205
00:09:07,530 --> 00:09:09,620
That's what the net
torque would be.

206
00:09:09,620 --> 00:09:12,660
And then we would get it, and it
would keep doing that until

207
00:09:12,660 --> 00:09:14,860
you get to the vertical
configuration.

208
00:09:14,860 --> 00:09:19,730


209
00:09:19,730 --> 00:09:22,680
So at the vertical
configuration, the circuit on

210
00:09:22,680 --> 00:09:24,800
the top stays exactly
the same.

211
00:09:24,800 --> 00:09:29,440


212
00:09:29,440 --> 00:09:31,850
I'm trying my best to
draw this properly.

213
00:09:31,850 --> 00:09:34,190
At the vertical configuration
one of two things can happen,

214
00:09:34,190 --> 00:09:37,590
and probably the best thing is
that we actually lose contact

215
00:09:37,590 --> 00:09:38,820
with the two leads.

216
00:09:38,820 --> 00:09:42,600
So maybe the actual current
stops flowing when we're in

217
00:09:42,600 --> 00:09:43,790
the vertical configuration.

218
00:09:43,790 --> 00:09:44,640
I'll do it in the same color.

219
00:09:44,640 --> 00:09:48,790
So when we're vertical
we just see the top.

220
00:09:48,790 --> 00:09:50,070
We see this.

221
00:09:50,070 --> 00:09:51,960
And then we see it pops
out a little bit.

222
00:09:51,960 --> 00:09:55,030
And then we see this
arm right there.

223
00:09:55,030 --> 00:09:57,560
And then we see that pole that's
maybe holding it or

224
00:09:57,560 --> 00:10:00,600
that's helping it rotate.

225
00:10:00,600 --> 00:10:02,260
But we're still having
some-- you know,

226
00:10:02,260 --> 00:10:03,270
the current has ceased.

227
00:10:03,270 --> 00:10:05,580
So there's not going to be any
torque, no force through the

228
00:10:05,580 --> 00:10:09,070
magnetic field, because we've
lost touch at that point.

229
00:10:09,070 --> 00:10:10,630
Because these things
kind of point out.

230
00:10:10,630 --> 00:10:14,920
Hopefully you could visualize
how to build such a thing.

231
00:10:14,920 --> 00:10:17,920
And we're still rotating in this
direction because of some

232
00:10:17,920 --> 00:10:20,810
type of rotational inertia.

233
00:10:20,810 --> 00:10:23,350
Then this is what the
interesting part is.

234
00:10:23,350 --> 00:10:27,140
What happens when we rotate
more than 90 degrees?

235
00:10:27,140 --> 00:10:29,555
And I just realized that I'm
pushing over 10 minutes, so

236
00:10:29,555 --> 00:10:32,860
you can think about that a
little bit while I stop here

237
00:10:32,860 --> 00:10:34,610
and continue this in
the next video.

238
00:10:34,610 --> 00:10:35,860
See

239
00:10:35,860 --> 00:00:00,000