I f you are walking along a tightly stretched rope and do not wish to fall off,

Question

If you are walking along a tightly stretched rope and do not wish to fall off, the problem is not placing your feet on the rope rather it is to avoid tipping over. To tip is to rotate, to experience an angular acceleration. If you want to reduce your angular acceleration you should increase your moment of inertia relative to your center of mass or, if you prefer, your feet. Holding a balancing pole can do this.

You are to design your own balancing pole. You can carry a total of 6kg. There are two types of pieces you can use. Rod sections are 1m in length and have a mass of 2kg. They can be screwed together to make a longer pole if you wish. Lead balls are small ( about 5cm in diameter ) and, if you wish they can be screwed to the end or ends of rods. Which balancing aid will be most beneficial?

(a) Three rod sections made into a 3m long pole which is held in the middle

(b) Three pole sections held together to make a 1m long fatter pole - this is held in the middle.

(c) One rod section with a lead ball at either end which is held in the middle

(d) Three lead balls skillfully juggled as you walk across the rope

(e) Three lead balls stuffed into your pockets

Explanation / Answer

for a:
Moment of inertia = mass * length^2/ 12 = 6*3^2/12 = 4.5 Kgm^2
for b:
Moment of inertia = mass * length^2/ 12 = 6*1^2/12 = 0.5 Kgm^2
for c:
Moment of inertia = I of rod + 2*I of ball
= m1* L^2/ 12 + 2*m*(L/2)^2
=2*1^2/12 + 2*2*(1/2)^2
=1.167 Kg/m^2
for d:
Moment of inertia:0
for e:
Moment of inertia = 0

So answer is a

I have used moment of inertia of a rod along its centre = mass * length^2/ 12

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