A 13-cm-diameter cd has a mass of 25 g . part a what is the cd's moment of inertia for rotation about a perpendicular axis through its center?

Answers

Answer 1
Answer: For a disc, the moment of inertia about the perpendicular axis through the center is given by 0.5MR^2. where M is the mass of the disc and R is the radius of the disc. For the axis through the edge, use parallel axis theorem. I = I(axis through center of mass) + M(distance between the axes)^2 = 0.5MR^2 + MR^2 (since the axis through center of mass is the axis through the center) = 1.5 MR^2
Answer 2

The cd's moment of inertia for rotation about a perpendicular axis through its center is about 5.3 × 10⁻⁵ kg.m²

[tex]\texttt{ }[/tex]

Further explanation

Let's recall Angular Momentum and Moment of Inertia of Cylinder formula as follows:

[tex]\boxed {L = I \omega}[/tex]

where:

L = angular momentum ( kg.m²/s )

I = moment of inertia ( kg.m² )

ω = angular frequency ( rad/s )

[tex]\texttt{ }[/tex]

[tex]\boxed { I = \frac{1}{2} M R^2 }[/tex]

where:

I = moment of inertia ( kg.m² )

M = mass of object ( kg )

R = radius of object ( m )

[tex]\texttt{ }[/tex]

Given:

mass of cd = M = 25 g = 0.025 kg

diameter of cd = d = 13 cm = 0.13 m

radius of cd = R = d/2 = 0.13/2 = 0.065 m

Asked:

moment of inertia = I = ?

Solution:

[tex]I = \frac{1}{2} M R^2[/tex]

[tex]I = \frac{1}{2} \times 0.025 \times 0.065^2[/tex]

[tex]\boxed{I = 5.3 \times 10^{-5} \texttt{ kg.m}^2}[/tex]

[tex]\texttt{ }[/tex]

Learn moreImpacts of Gravity : https://brainly.com/question/5330244Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454The Acceleration Due To Gravity : https://brainly.com/question/4189441

[tex]\texttt{ }[/tex]

Answer details

Grade: High School

Subject: Physics

Chapter: Circular Motion

A 13-cm-diameter Cd Has A Mass Of 25 G . Part A What Is The Cd's Moment Of Inertia For Rotation About

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So we could find the solution by estimation through rounding off.

 

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According to question ,pounds of almonds in $3.49 = 1 pound

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