The wheel, rotating equally slowly, reduced its frequency from V = 300 rpm to V2 = 100 rpm in t = 1 min

The wheel, rotating equally slowly, reduced its frequency from V = 300 rpm to V2 = 100 rpm in t = 1 min. Find the angular acceleration of the wheel and the number of revolutions made by it during this time.

v1 = 300 rpm = 5 rpm.

v2 = 100 rpm = 1.7 rpm.

t = 1 min = 60 s.

ε -?

n -?

The angular acceleration ε is determined by the formula: ε = (w1 – w2) / t, where w1, w2 are the initial and final angular velocity.

w1 = 2 * P * v1.

w2 = 2 * P * v2.

ε = (2 * P * v1 – 2 * P * v2) / t = 2 * P * (v1 – v2) / t.

ε = 2 * 3.14 * (5 r / s – 1.7 r / s) / 60 s = 0.35 rad / s2.

Find the angle of rotation φ by the formula: φ = w1 * t – ε * t2 / 2.

φ = 31.4 rad / s * 60 s – 0.35 rad / s2 * (60 s) 2/2 = 1254 rad.

The number of wheel revolutions n is found by the formula: n = φ / 2 * P = 1254 rad / 6.28 rad = 200 rpm.

Answer: ε = 0.35 rad / s2, n = 200 vol.