Question

6. conical surface of constant density find the moment of iner?tia about the z-axis of a thin shell of constant densthe cone 4x 2 4y 2 - z 2

Answer 1

The moment of inertia about the y-axis of the thin semicircular region of constant density is given below.

What is rotational inertia?

• Inertia of rest: The inability of a body to change by itself its state of rest is called inertia of rest. Inertia of direction: The inability of a body to change by itself its direction of motion. Inertia of motion: The inability of the body to change by itself its state of motion is called inertia of motion

1. You tend to move forward when a sudden break is applied.
2. You feel a backward force when the bus moves quickly from rest.
3. Dusting bed with a broom removes dust due to inertia of rest.
4. when you shake a branch the leaves get detached.

• According to Newton's first law of motion, an object with a given velocity maintains that velocity unless acted on by an external force. Inertia is the property of matter that makes this law hold true.
• Any item that can be turned has rotational inertia as a quality. It's a scalar value that indicates how complex it is to adjust an object's rotational velocity around a certain axis.
• Then the moment of inertia about the y-axis of the thin semicircular region of constant density will be.
• When a car makes a sharp turn at a high speed, the driver tends to get thrown to another side due to inertia of direction.
• The spark coming out of a grinding stone is tangential to the rotating stone due to directional inertia.
• The mud from the wheels of a moving vehicle flies off tangentially.

$I_{y} = (\frac{1}{8}) \pi r^{4}$

x = r cos θ

y = r sin θ

dA = r dr dθ

Then the moment of inertia about the x-axis will be

To learn more about inertia refer to:

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