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Chapter 9: Q18P (page 378)

If an object’s rotational kinetic energy is 50 J and it rotates with an angular speed of 12 rad/s, what is the moment of inertia?

Short Answer

Expert verified

The moment of inertia is,0.69kg.m2 .

Step by step solution

01

Identification of the given data

The given data can be listed below as,

  • The kinetic energy of the object is,Krot=50J.
  • The angular speed of object is, ω=12rad/s
02

Significance of rotational kinetic energy

The rotational kinetic energy of a rotating object can be expressed as half the product of the object's angular velocity and its moment of inertia about its axis of rotation.

03

Determination of the moment of inertia

The relation of rotational kinetic energy is expressed as,

Krot=12Iω2 ...(i)

Here Krotis the rotational kinetic energy, ωis the angular speed andIis the moment of inertia.

Substitute 50 J for Krot, and 12 rad/s for ωin the equation (i).

role="math" localid="1657850631785" 50J=12×I×12rad/s2I=0.69kg.m2

Hence the moment of inertia is, 0.69kg.m2.

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