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SMOKEY2112 SMOKEY2112
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7 years ago
at 4 o'clock.  Assume the hand has a mass of 15 kg and a length of 1.5 m,  and the mass is uniformly distributed.
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datty117datty117
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7 years ago
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To work this out, all you need to do is work out the distance (horizontally) from the centre of the clock to the centre of gravity of the hour hand. The centre of gravity of the hand is at the middle, due to the fact the mass is evenly distributed. Therefore, to find the horizontal distance from the centre of the clock to the middle of hour hand (obviously less than 75cm), we need to use some trigonometry:

1 hour = 30degrees
length of hypotenuse = 75cm (half the length of the hour hand)
horizontal distance to centre of gravity of hour hand = 75cm * cos30 = 65cm

Next, we want to work out the torque on the hour hand.

Torque = mass * distance.

Therefore, the torque on the hour hand = mass * horizontal distance we have calculated.
 = 15kg * 65cm
 (converting 15kg into a force = 15kg * 9.81m/s2)
 = 147N * 0.65m
 = 95.6 N.m

Might want to do some rounding depending on what value of gravity you are meant to be using.
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