Problem: Consider a particle of mass m that is revolving with angular speed ω around an axis. The perpendicular distance from the particle to the axis is r. (Figure 1) 1.) Find the kinetic energy K of the rotating particle. Express your answer in terms of m, r, and ω.2.) Find the moment of inertia Ihoop of a hoop of radius r and mass m with respect to an axis perpendicular to the hoop and passing through its center. Express your answer in terms of m and r.

FREE Expert Solution

Kinetic energy:

K=12mv2

1.

From the equation, we get v as:

v = rω

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Problem Details

Consider a particle of mass m that is revolving with angular speed ω around an axis. The perpendicular distance from the particle to the axis is r. (Figure 1) 

1.) Find the kinetic energy K of the rotating particle. Express your answer in terms of m, r, and ω.

2.) Find the moment of inertia Ihoop of a hoop of radius r and mass m with respect to an axis perpendicular to the hoop and passing through its center. Express your answer in terms of m and r.

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Our tutors have indicated that to solve this problem you will need to apply the Intro to Rotational Kinetic Energy concept. You can view video lessons to learn Intro to Rotational Kinetic Energy. Or if you need more Intro to Rotational Kinetic Energy practice, you can also practice Intro to Rotational Kinetic Energy practice problems.