The beater of the flax harvester rotates with a constant angular acceleration of 2, m l \ s ^ 2.

The beater of the flax harvester rotates with a constant angular acceleration of 2, m l \ s ^ 2. Determine the full acceleration of the beater 1 second (s) after the start of the movement. Beater diameter 0.45m.

To calculate the full acceleration of the beater, we will use the formula: a = √ (an ^ 2 + aτ ^ 2) = √ ((ω ^ 2 * R)) ^ 2 + (R * ε) ^ 2) = √ (((ε * t) ^ 2 * R)) ^ 2 + (R * ε) ^ 2) = √ (ε ^ 4 * t ^ 4 * R ^ 2 + R ^ 2 * ε ^ 2).

Variables: ε – angular acceleration of the beater (const, ε = 2 rad / s2); t is the considered time of movement of the beater (t = 1 s); R is the radius of the beater (R = 0.5d = 0.5 * 0.45 = 0.225 m).

Calculation: a = √ (ε ^ 4 * t4 * R ^ 2 + R ^ 2 * ε ^ 2) = √ (24 * 14 * 0.225 ^ 2 + 0.225 ^ 2 * 2 ^ 2) = √ (0.81 + 0.2025) = √1.0125 ≈ 1 m / s2.

Answer: After 1 second, the full acceleration of the beater will be 1 m / s2.




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