determine the following for the sphere when it is at the bottom of the plane: its translational kinetic energy

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05-12-2022
Physics

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determine the following for the sphere when it is at the bottom of the plane: its translational kinetic energy

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jaiswaljyoti jaiswaljyoti · Answer 1 · 2022-12-09T03:32:16-05:00

At the bottom of the inclined plane, the total potential energy is converted into translational kinetic energy as shown in the below figure.

The sphere has two kinds of kinetic energy: translational and rotational. The translational kinetic energy is given by the usual equation: 1/2 mv^2.

The rotational energy is 1/2 Iω^2.

At the bottom of the inclined plane, the total potential energy is converted into translational kinetic energy as shown in the bellow figure

For a solid sphere I = 2/5 mr^2,

where r is the radius of the sphere. the last term of the rotational kinetic energy is the angular velocity, which may be expressed in radians/second or other units like the one shown below: linear velocity units/linear units. In these last cases, you have to change the angular velocity to linear velocity.

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