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Angular Acceleration Formula:
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Angular acceleration (α) is the rate of change of angular velocity with respect to time. It describes how quickly an object's rotational speed is changing and is measured in radians per second squared (rad/s²).
The calculator uses the fundamental rotational dynamics formula:
Where:
Explanation: This formula is the rotational equivalent of Newton's second law (F = ma), where torque replaces force, moment of inertia replaces mass, and angular acceleration replaces linear acceleration.
Details: Calculating angular acceleration is crucial in mechanical engineering, robotics, aerospace, and physics for designing rotating systems, analyzing rotational motion, and predicting system behavior under applied torques.
Tips: Enter torque in Newton-meters (Nm) and moment of inertia in kilogram-meter squared (kg·m²). Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is the difference between angular and linear acceleration?
A: Linear acceleration describes changes in straight-line velocity, while angular acceleration describes changes in rotational speed. They are related but describe different types of motion.
Q2: How is moment of inertia different from mass?
A: Mass measures resistance to linear acceleration, while moment of inertia measures resistance to angular acceleration. It depends on both mass and how that mass is distributed relative to the axis of rotation.
Q3: What are typical units for angular acceleration?
A: The standard SI unit is radians per second squared (rad/s²), but degrees per second squared (°/s²) is also used in some applications.
Q4: Can angular acceleration be negative?
A: Yes, negative angular acceleration indicates deceleration or rotation in the opposite direction to the initial angular velocity.
Q5: What factors affect moment of inertia?
A: Moment of inertia depends on the object's mass, shape, and the axis about which it rotates. Objects with mass farther from the axis have higher moment of inertia.