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Torque To Acceleration Formula:
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The Torque To Acceleration formula calculates the linear acceleration produced by a torque applied to a mass at a certain radius from the axis of rotation. This formula is derived from Newton's second law for rotational motion and is fundamental in mechanical engineering and physics.
The calculator uses the formula:
Where:
Explanation: The formula shows that acceleration is directly proportional to the applied torque and inversely proportional to both the mass and the radius from the axis of rotation.
Details: Calculating acceleration from torque is essential for designing mechanical systems, analyzing rotational motion, determining performance characteristics of engines and motors, and solving problems in dynamics and kinematics.
Tips: Enter torque in N·m, mass in kg, and radius in m. All values must be positive numbers greater than zero for valid calculation.
Q1: What units should I use for this calculation?
A: Use Newton-meters (N·m) for torque, kilograms (kg) for mass, and meters (m) for radius to get acceleration in m/s².
Q2: Does this formula account for friction?
A: No, this is an ideal formula that assumes no friction or other resistive forces. In real-world applications, actual acceleration may be less due to friction.
Q3: Can this formula be used for angular acceleration?
A: No, this formula calculates linear acceleration. For angular acceleration, use α = τ/I, where I is the moment of inertia.
Q4: What if the mass is distributed rather than point mass?
A: This formula assumes the mass is concentrated at the radius r. For distributed masses, you would need to use the moment of inertia instead of m·r.
Q5: Is this formula valid for all types of motion?
A: This formula applies specifically to cases where torque produces linear acceleration of a mass at a fixed radius from the rotation axis, typically in systems like pulleys or gears driving linear motion.