Clock movement and angular velocity questions

[cherica123]

Hey, I just got this "review" sheet for math and am not sure how to do the following questions. Please help!

On this one, I just don't know where to begin.....
1.) If it is 10 AM, how many minutes would you have to wait until both hands of the clock were pointing in opposite directions?

(This isnt just 10:30, we have to take into account how much the hour hand moves too.)


2.) A wheel on a car has a radius of 30 cm and the car was traveling at 60 km/h. What is the angular velocity in radians/min?

For this, I started with
v=rw
w= r/v

which gives me the start of (30cm)/(60km/h). I have to multiply by 100000 to convert cm to km, giving me
(3000000km)/(60km/h).
Somewhere I believe I have to convert hours to minutes but im confused by the
km
km
hr

fraction setup. What/where to I multiply/divide by 60 to make the conversion? And once I do that, does that give me rad/min, or is there more to do on this problem?
Or did I just do it entirely wrong?


Thanks!

 

[neohashi]

I'll give you a few hints..

1.)
So you have two clock hands: hours and minutes.. look at them as two linear functions.. h(x) and m(x) and solve the equation:

h(x) = m(x) + 30
or just
h(x) = x + 30

Figure out what h(x) should be.

The 30 min offset is just to make the hands point in upperset directions.

2.)
you are quite off on this one...

for startes the circumference of your wheel is 2*pi*radius

about conversion.. 60km/h = (60*1000*100)/60 = 100000cm/min .. so if your wheel was 100 cm in circumference it would turn at 100000/100 = 1000 rpm.. 1000*2*pi ~= 6283 radians/min