## Rotational Kinetic Energy and Moment of InertiaA grindstone with a radius of 0.610 m is being used to sharpen an ax. If the linear speed of the stone relative to the ax is 1.50 m/s and the stone's rotational kinetic energy is 13 J, what is the moment of inertia?### Problem Analysis:The sketch shows the grindstone spinning with an angular speed \( \omega \), which is not given in the problem statement. We do know, however, that the linear speed of the grindstone at its rim is \( v = 1.5 \, \text{m/s} \) and that its radius \( r = 0.610 \, \text{m} \). At this rate, the stone has kinetic energy of 13 J.### Strategy:Rotational kinetic energy and moment of inertia are related by:\[\text{Kinetic Energy} = \frac{1}{2} I \omega^2\]Solving for \( I \),\[I = \frac{2K}{\omega^2}\]We are not given \( \omega \), but we can find it from the connection between linear and angular speed,\[v = r \omega\]Thus we begin by finding \( \omega \), along with Kinetic Energy (K.E) to find \( I \).### Diagram Explanation:The diagram displays a grindstone with:- A radius labeled as \( = 0.610 \, \text{m} \).- Linear speed at the rim labeled as \( v = 1.50 \, \text{m/s} \).- An angular speed \( \omega \) shown as a symbol near the axis.- An ax contacting the grindstone. The diagram helps visualize the rotation and the relationship between the linear speed and the angular speed.

Given:- Radius (r) = 0.610 m Linear speed (v) = 1.50 m/s Kinetic energy (K) = 13 J Angular speed…

Answered: 2) Rotational kinetic energy and Moment…

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