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

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

Solutions

Expert Solution

Given

Initial angular speed (?₀ ) = 0

Final angular speed (? ) = 44.4rad/s

Radius of ball (r ) = 4.3 cm

= 0.043 m

Angular acceleration (?) = 245 rad/s²

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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 incline L = ? r

L = 4.023rad x 0.043 m

= 0.173 m

genius_generous answered 1 year ago

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