Determine the acceleration of a material point during its uniform rotation, if in Δt = 1 s

| August 8, 2021 | education

Determine the acceleration of a material point during its uniform rotation, if in Δt = 1 s it has passed 1/6 of the circumference, having a linear velocity modulus v = 10 m / s.

t = 1 s.

S = L / 6.

V = 10 m / s.

a -?

When moving in a circle, centripetal acceleration, and is determined by the formula: a = V ^ 2 / R, where V is the linear speed of movement, R is the radius of the circle.

We express the speed of movement V by the formula: V = S / t, where S is the path traveled by the body, t is the time of movement.

The circumference L is determined by the formula: L = 2 * P * R.

V = 2 * P * R / 6 * t = P * R / 3 * t.

R = V * 3 * t / P.

a = V ^ 2 * P / V * 3 * t = V * P / 3 * t.

a = 10 m / s * 3.14 / 3 * 1 s = 10.5 m / s ^ 2.

Answer: the body moves with a centripetal acceleration a = 10.5 m / s ^ 2.



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