A hollow cylinder and a solid cylinder having the same mass and diameter are rel

Question

A hollow cylinder and a solid cylinder having the same mass and diameter are released from rest simultaneously at the top of an inclined plane. Which reaches the bottom first? Explain. Animals that depend on being able to run fast have slender lower legs with flesh and muscle concentrated higher up near the shoulder. Why is this distribution of mass advantageous? Why is it that a child playing tightrope on a railroad track rail finds it easier to maintain her balance when her arms are fully outstretched to the sides? A diatomic molecule can be thought of as something like a weight lifting barbell with most of the mass of the molecule concentrated in two spherical (radius r) mass separated by a distance d>>r.. About what axis through the center of mass of the molecule would the moment of inertia be the least? About what axis through the center of mass of the molecule would the moment of inertia be the greatest?

Explanation / Answer

1)

The solid goes faster because it has a smaller moment of inertia.

The problem with the hollow sphere is that all of its weight is on the outer circumference which means that a lot of the gravitational energy is used to increase the rotation rather than the speed of the cylinder.

2)

The muscles that control the majority of the movement are the ones closest to the body, in humans these would be the thigh muscles, and those of the upper arm (biceps and triceps). The thigh muscles contract to swing the front of the leg forwards, so the bigger these are the faster you can swing the leg forwards.

When you're running your body is moving fast, so you need to be able to support it before your face meets the floor. you need to be able to swing your leg forwards, then stop it and place your foot down before your centre of mass gets in front of it. It's easier to stop a small weight than a large weight, so heavily muscled ankles would be a hindrance, it woul take you longer to stop and place your foot on the ground, which could mean the difference between getting away and getting

3)

Any imbalance that moves her centre of gravity outside of the perpendicular line above the rail, will provide a small ( initially small ) torque that tries to accelerate the body about the turning point ( her feet ). She will have some short time in which to provide a balancing counter torque to bring her back to equilibrium, usually by throwing out and arm or leg to the side opposite to the rotation.
With extended arms the childs moment of inertia about the turning point is increased. This will mean that for any given unbalancing torque the resulting angular acceleration is smaller and so more time is made available for adjustments... it becomes easier to balance... just remember that balance is an ongoing dynamic process, subject to continuous perturbations that require compensation. And keep your arms out.

We get fined if we are caught walking on the tracks.

4)

Least: An axis that can be thought of running along the "bar" of the barbell going through the center of mass and each of the center of masses of the end spheres. Or lying in the plane of the "barbell"

Most: An axis through the center of mass of the system and perpendicular to the plane that the "barbell" occupies.

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