Question

body is rotating with uniform angular velocity about and axis. Establish the formula for its

kinetic energy of rotation. Define moment of inertia of the body with respect to the axis of

rotation on this basis. ​

Answer 1

Explanation:

The rotational kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy.

Kinetic Energy of Rotation: Things that roll without slipping have some fraction of their energy as translational kinetic and the remainder as rotational kinetic. The ratio depends on the moment of inertia of the object that’s rolling.

E

rotational

=

1

2

I

ω

2

,

where

ω

is the angular velocity and

I

is the moment of inertia around the axis of rotation.

The mechanical work applied during rotation is the torque (

τ

) times the rotation angle (

θ

):

W

=

τ

θ

.

The instantaneous power of an angularly accelerating body is the torque times the angular velocity:

P

=

τ

ω

.

Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion:

E

translational

=

1

2

mv

2

.

In the rotating system, the moment of inertia takes the role of the mass and the angular velocity takes the role of the linear velocity.

Answer 2

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Kinetic Energy of Rotation: Things that roll without slipping have some fraction of their energy as translational kinetic and the remainder as rotational kinetic. The ratio depends on the moment of inertia of the object that’s rolling.

Erotational=12Iω2,where ω is the angular velocity and I is the moment of inertia around the axis of rotation.

The mechanical work applied during rotation is the torque (τ) times the rotation angle (θw=τθ)