Easiest Cylinder to Balance - angular acceleration

[mike115]

Homework Statement

24. A person tries to balance vertically each of three long uniform cylinders with equal radii on the end of his finger:


* A wood cylinder of mass m and length L with moment of inertia I
* A bamboo cylinder of mass m and length 3L with moment of inertia 9I
* A concrete cylinder of mass 4m and length 2L with moment of inertia 16I


Which object is the easiest to balance and why?

A. The wood cylinder is easiest to balance because it has the smallest moment of inertia.
B. The concrete cylinder is easiest to balance because it has the largest moment of inertia.
C. The concrete cylinder is easiest to balance because it is the most massive.
D. The bamboo cylinder is easiest to balance because it has the least density.
E. The bamboo cylinder is easiest to balance because it is longest.

Correct Answer: E

Homework Equations

net torque = I*alpha

The Attempt at a Solution

I don't understand how the answer is E. I thought the object with the largest moment of inertia would have the smallest angular acceleration. It just seems to me that if the cylinder is longer, the gravitational force will act at a further distance from the support point which would only increase the net torque.

 

[physixguru]

It is actually harder to balance small objects (such as pencils) than large objects (such as broom handles). Tall objects have a higher centre of mass. Basically this means that they will begin falling slowly, giving you a little more time to quickly correct your body to keep the object upright.

 

[Moetasim]

Can someone explain why E is the correct answer?

The correct answer is E because the bamboo cylinder has the least density, which means it has less mass per unit length compared to the other cylinders. This results in a smaller moment of inertia, making it easier to balance because it requires less torque to achieve the same angular acceleration. Additionally, the longer length of the bamboo cylinder also contributes to its lower moment of inertia, making it the easiest to balance.