The shaft starts rotating from a state of rest and makes N = 50 revolutions during the first t = 10 s.

The shaft starts rotating from a state of rest and makes N = 50 revolutions during the first t = 10 s. Assuming the rotation of the shaft to be uniformly accelerated, determine the angular acceleration.

To find the value of the angular acceleration of the specified shaft, we will use the equality: 2 * Π * N = φ (angular displacement of the shaft) = ε * t ^ 2/2, whence we express: ε = 4 * Π * N / t ^ 2.

Variables: N is the number of revolutions of the specified shaft (N = 50 revolutions); t – duration of shaft rotation (t = 10 s).

Let’s make a calculation: ε = 4 * Π * N / t ^ 2 = 4 * 3.14 * 50/10 ^ 2 = 6.28 rad / s2.

Answer: The angular acceleration of the specified shaft is 6.28 rad / s2.