# Clock Torque Question

1. Mar 4, 2013

### AeroVector

I have attempted this a few times, I got these answers--- 655.44N and 345.144N
If anyone can solve this for me it would be appreciated

The hour and minute hands of the clock in
the famous Parliament Clock Tower in London are 1.7 m and 3.4 m long and have masses
of 89 kg and 60 kg, respectively
Calculate the magnitude of the torque
around the center of the clock due to the
weight of these hands indicating 3 h and
1 min; i.e., 3:1 o’clock. Assume the clock
hands can be modeled as uniform thin rods
and at 3:00 o’clock, the hour hand is precisely
90◦
from the vertical. The acceleration of
gravity is 9.81 m/s
2
.
Answer in units of N · m

2. Mar 4, 2013

### Maiq

I got 1482.74N*m and 208.97N*m. How did you solve these?

3. Mar 4, 2013

### AeroVector

(360 deg/rev) / [12hr * 60 min/hr/rev] = 0.5° / min

Th = mg(l/2)cosθ
Th = 60(9.81)(1.7/2)cos(-0.5)
Th =500 Nm

360 deg/rev / 60 min/rev = 6 degrees/min
90 - 6 = 84° from horizontal

Tm = mg(l/2)cosθ
Tm = 89(9.81)(3.4/2)cos84

Tm = 155 Nm

4. Mar 4, 2013

### AeroVector

155+ 500 =650Nm 600-144 = 345Nm thats how i got those answers

5. Mar 4, 2013

### Maiq

My answers were the torques for the hour hand and minute hand. I messed up the one for the Tm though but i fixed it and had the same answer as you also i forgot to divide my answers by 2 so the Th I had is 741.37. Torque is force multiplied by the perpendicular distance so for Th you just had to do mg(L/2).
Where did the 600-144 come from?

6. Mar 4, 2013

### Maiq

Actually my Th was wrong too. Sorry I mixed up the masses. so I got 500 also for that one

7. Mar 4, 2013

### AeroVector

So what would I do with the 500 and 155? I added them together and it was wrong do it take 500-155 or 155-500?

8. Mar 5, 2013

### lep11

Counter-clockwise moments (or torques in the English speaking world?) are positive and clockwise moments are negative so all you have to do is to think which direction would the hands of the clock swing due to gravity if they could swing freely. The hour hand would swing clockwise due to gravity and the minute hand would swing counter-clockwise because of gravity pulling it. Did my explanation make sense to you?

Last edited: Mar 5, 2013
9. Mar 5, 2013

### AeroVector

I put in -345 , 655 and 345 and all of them were wrong so far

10. Mar 5, 2013

### Staff: Mentor

Hi lep11. It sounds like you live in a fascinating land. Contrast your experience with this: at 3:01 the hands of plain old English speaking clocks are located on the same side of the vertical, and both exert clockwise torque on their shaft.

11. Mar 5, 2013

### Staff: Mentor

That looks right.

What's the torque for the minute hand?

12. Mar 5, 2013

### lep11

Yes, it may sound like that because I mistakenly thought the time was 2:59 instead of 3:01, sorry.

13. Mar 5, 2013

### CWatters

I got the slightly different figure of 742.13 N.m and 104.59 N.m. Might make a difference to the rounding.

14. Mar 5, 2013

### AeroVector

In the end I ended up getting those torques, thank you to everyone for your help and input!