A 4.3- cm-radius ball rolls down an inclined plane from rest at the top. The angular...

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Physics

A 4.3- cm-radius ball rolls down an inclined plane from rest atthe top. The angular acceleration of the rolling ball about itscenter is 245 rad/s², and its angular speed at thebottom is 44.4 rad/s. How long is the plane?

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4.4 Ratings (819 Votes)

GivenÂ Â

Initial angular speedÂ Â (?₀ ) = 0

Final angular speedÂ Â (? )Â Â Â =Â Â Â 44.4rad/s

Radius of ballÂ Â Â Â Â Â Â Â Â Â Â Â (r )Â Â Â Â =Â Â Â 4.3 cmÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =Â Â Â 0.043 m

Â Â Â

Angular accelerationÂ Â Â Â (?)Â Â Â Â =Â Â 245 rad/s²

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Â Â Â

The third equation of motion in rotational motion is

?²=?₀² + 2 ? ?

(44.4 rad/s)² =(0)² + 2 ( 245 rad/s²) ( ? )

?The angular displacement (?) =4.023 rad

Length of inclineÂ Â Â LÂ Â Â =Â Â Â ? r

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â LÂ Â Â =Â Â 4.023rad x 0.043 m

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 0.173 m

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