Question

A wheel with radius 3m rolls at 18 rad/s.How fast is a point on the rim of the wheel rising when the point is pi/3 radians above the horizontal(and rising)?

Answer 1

The two variables here are \(\theta\), the angle of rotation and \(x\), the height of the point.

Answer 2

The relationship between the two would be \(x=\sin\theta\)

Answer 3

You are given \(\theta\) and \(d\theta / dt\) and asked to find \(dx/dt\).

Answer 4

@hturkcom Does this analysis seem correct to you?

Answer 5

Yes

Answer 6

Wait, there is on mistake. I should have included the radius.

Answer 7

asking m/s

Answer 8

Can you correct my mistake?

Answer 9

I didn't get it.

Answer 10

What is the height of the point given theta?

Answer 11

3m

Answer 12

So you are saying the point is always at 3m even when the wheel is spinning?

Answer 13

solution supposed to 27.0 m/s.I cannot find this resolution.

Answer 14

I'm not asking for the solution. I'm asking for the relationship between \(x\) the height of the point, and \(\theta\) the angle of the point.

Answer 15

\[\pi/3\]

Answer 16

60

Answer 17

Nope. Let me draw a picture.

Answer 18

What is the equation which describes the relationship between \(x\) and \(\theta\)?

Answer 19

Do you know trigonometry?

Answer 20

0+3cos(pi/3)(18rad/sec)

Answer 21

=27

Answer 22

Do you understand where that comes from?

Answer 23

\[\sin \theta= \frac{ y }{ r } ,y=rsin \theta,\frac{ dy }{dt }=\frac{ dr }{ dt } \sin \theta+rcos \theta \frac{ d \theta }{ dt }=0+3\cos(\frac{ \pi }{ 3 })(18)=27\]

Answer 24

What do you think do I know it?:)