The body rotates uniformly with an initial angular velocity of 5 s-1 and an angular acceleration of 1 s-2.

The body rotates uniformly with an initial angular velocity of 5 s-1 and an angular acceleration of 1 s-2. How many revolutions will the body make in 10 seconds?

To find the number of revolutions of a taken body in 10 s of movement, we will use the equality: 2 * Π * N = φ (angle of rotation) = ω0 * t + ε * t ^ 2/2, whence we express: N = (ω0 * t + ε * t ^ 2/2) / (2 * Π).

Variable values: ω0 – initial angular velocity (ω0 = 5 rad / s); t – elapsed time (t = 10 s); ε – angular acceleration (ε = 1 rad / s2).

Let’s perform the calculation: N = (ω0 * t + ε * t ^ 2/2) / (2 * Π) = (5 * 10 + 1 * 10 ^ 2/2) / (2 * 3.14) = 15.92 turnover ≈ 16 turns.

Answer: In 10 seconds, the taken body made 16 revolutions.