# Find the linear speed of motion of the center of a ball that rolled without sliding with an inclined plane 0.5 meter high

October 11, 2021 | education

| Given: h (height of the inclined plane) = 0.5 m; g (acceleration due to gravity) ≈ 10 m / s2.

Let us express the linear velocity of the center of mass: En = m * g * h = Ek (kinetic energy of rotational and translational motions) = I * ω ^ 2/2 + m * V ^ 2/2, where I (moment of inertia of the ball) = 2 / 5 * m * R ^ 2; ω (angular velocity) = V / R.

m * g * h = 2/5 * m * R ^ 2 * (V / R) ^ 2/2 + m * V ^ 2/2.

g * h = V ^ 2/5 + V2 / 2.

g * h = 7V ^ 2/10.

V2 = 10 * g * h / 7 and V = √ (10 * g * h / 7).

Calculation: V = √ (10 * 10 * 0.5 / 7) = 2.67 m / s.

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