Final answer:
The angular acceleration of the crankshaft is approximately 1653 rad/s². None of the given option is correct. Although we can consider Option A as it is nearest to 1653 rad/s².
Step-by-step explanation:
To find the angular acceleration of the crankshaft, we can use the formula:
angular acceleration = (final angular velocity - initial angular velocity) / time
Given that the crankshaft goes from rest (0 rpm) to 3180 rpm in 3.2 s, we can convert the final and initial angular velocities to rad/s by multiplying by 2π/60:
Final angular velocity = 3180 rpm × (2π/60) rad/s = 334π rad/s
Initial angular velocity = 0 rpm × (2π/60) rad/s = 0 rad/s
Substituting the values into the formula:
angular acceleration = (334π rad/s - 0 rad/s) / 3.2 s ≈ 1653 rad/s²
Therefore, the angular acceleration of the crankshaft is approximately 1653 rad/s².
To determine the angular acceleration of the crankshaft, we employ the formula: angular acceleration = (final angular velocity - initial angular velocity) / time. As the crankshaft transitions from rest (0 rpm) to 3180 rpm in 3.2 seconds, we convert these velocities to rad/s by multiplying by 2π/60. The final angular velocity becomes 334π rad/s, while the initial angular velocity is 0 rad/s. Substituting these values into the formula yields an angular acceleration of (334π rad/s - 0 rad/s) / 3.2 s, approximately 1653 rad/s². This signifies the rate of change of angular velocity during the specified time interval, reflecting the crankshaft's acceleration in a rotational context.