The equation of rotation of a rigid body is φ = 2t2 + 3t. Determine the number of revolutions of the body

The equation of rotation of a rigid body is φ = 2t2 + 3t. Determine the number of revolutions of the body, angular velocity, angular acceleration 15 s after the start of rotation.

φ (t) = 2 * t ^ 2 + 3 * t.

t = 15 s.

N -?

w -?

ε -?

The angle of one complete revolution is 2 * п radians.

N = φ (t) / 2 * п.

φ (15 s) = 2 * (15 s) ^ 2 + 3 * (15 s) = 495 rad.

N = 495/2 * 3.14 = 78.8.

The dependence of the angular velocity on time is the derivative of the dependence of the angle on time: w (t) = φ (t) “.

w (t) = (2 * t ^ 2 + 3 * t) “= 4 * t + 3.

w (15 s) = 60 + 3 = 63 rad / s.

The dependence of the angular acceleration on time is the derivative of the dependence of the angular velocity on time: ε (t) = w (t) “.

ε (t) = (4 * t + 3) “= 4 rad / s2.

ε (15 s) = 4 rad / s2.

Answer: N = 78.8, w = 63 rad / s, ε = 4 rad / s2.