# Total angular momentum of hands of Big Ben

• DarkerStorm
In summary: Thanks for pointing that out. The difference between the two formulas for moment of inertia is because the hour hand is treated as a thin, long rod. So we use the formula for a rod about its center of mass, which is 1/12. The minute hand is also treated as a thin, long rod, but it is rotating about its endpoint, so we use the formula for a rod rotating about its endpoint, which is 1/3.In summary, the total angular momentum of the minute and hour hand of Big Ben in London, treated as long, thin rods, is 0.269791 kg · m^2/s and 0.0493228 kg · m^2/s respectively, with the difference in moment
DarkerStorm
Hello I just can't seem to get this problem right

## Homework Statement

The hour and minute hands of Big Ben in London are 2.6 m and 4.58 m long and have masses of 68.6 kg and 97 kg respectively. Calculate the total angular momentum of the minute and hour hand about the center point. Treat the hand as long, thin rod. Treat “into the clock” as the positive direction. Answer in units of kg · m2/s.

## Homework Equations

$$\omega = \frac{ 2\pi }{T}$$

$$I = \frac{1}{3} M R^2$$
$$I = \frac{1}{12} M R^2$$?

$$L = I \omega$$

## The Attempt at a Solution

Mmin= 68.6
Mhour = 97

lmin = 2.6
lhour = 4.58

$$\omega min = \frac{2\pi}{3600}$$
$$\omega hour = \frac{2\pi}{86400}$$

$$Imin = \frac{1}{3} Mmin lmin^2$$ = 154.579
$$Ihour = \frac{1}{3} Mhour lhour^2$$ = 678.237

$$Lmin = Imin \omega min$$ = 0.269791
$$Lhour = Ihour \omega hour$$ = 0.0493228

Your calculation looks all right, so probably you've just made a little mistake somewhere.

Are you sure you aren't switching the minute and hour hands somewhere halfway? The hour hand is 2.6 m and 68.6 kg and the minute hand is 4.58 m and 97 kg. Are you using that consistently?

You are giving two formulas for the moment of inertia, with 1/3 and 1/12 in front. Can you explain the difference?

Also, don't forget your units, especially in the final answer (what is the unit of angular momentum?)

Thanks I found out where I was wrong now, I was switching the mass numbers of minutes and hour hands.

## 1. What is the total angular momentum of the hands of Big Ben?

The total angular momentum of the hands of Big Ben is determined by the mass and velocity of the hands as they rotate around the clock face. It is also affected by external factors such as air resistance.

## 2. How is the total angular momentum of the hands of Big Ben calculated?

The total angular momentum can be calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The values for I and ω can be determined by measuring the mass and length of the hands, as well as the rate at which they rotate.

## 3. Does the total angular momentum of the hands of Big Ben change over time?

Yes, the total angular momentum of the hands of Big Ben can change over time due to various factors such as wear and tear on the hands or changes in air resistance. However, the overall value of the angular momentum will remain constant unless acted upon by an external force.

## 4. What is the significance of the total angular momentum of the hands of Big Ben?

The total angular momentum of the hands of Big Ben is significant because it represents the amount of rotational motion and energy in the system. It also plays a role in determining the stability and accuracy of the clock's timekeeping.

## 5. Can the total angular momentum of the hands of Big Ben be altered?

Yes, the total angular momentum of the hands of Big Ben can be altered by changing the mass or length of the hands, or by adjusting the rate at which they rotate. However, any changes made to the angular momentum must be done carefully to avoid affecting the accuracy of the clock's timekeeping.

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