A 3.4- cm-radius ball rolls down an inclined plane from rest at the top. The angular...

A 3.4- cm-radius ball rolls down an inclined plane from rest at the top. The angular acceleration of the rolling ball about its center is 275 rad/s2, and its angular speed at the bottom is 58.4 rad/s. How long is the plane?

Expert Solution

Given

Initial angular speed (ω₀ ) = 0

Final angular speed (ω ) = 58.4rad/s

Radius of ball (r ) = 3.4 cm

= 0.034 m

Angular acceleration (α) = 275 rad/s²

The third equation of motion in rotational motion is

ω²=ω₀² + 2 α θ

(58.4 rad/s)² =(0)² + 2 ( 275 rad/s²) ( θ )

∴The angular displacement (θ) =6.20 rad

Length of incline L = θ r

L = 6.20rad x 0.034 m

= 0.210m

genius_generous answered 2 years ago

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