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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. In rotational dynamics, it plays the same role as linear acceleration does in linear motion.
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 essential in mechanical engineering, robotics, automotive design, and physics. It helps determine how quickly objects can start or stop rotating, which is crucial for designing motors, gears, and rotating machinery.
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 valid calculation.
Q1: What is the difference between angular acceleration and linear acceleration?
A: Angular acceleration refers to changes in rotational speed (rad/s²), while linear acceleration refers to changes in straight-line speed (m/s²).
Q2: How is moment of inertia different from mass?
A: Moment of inertia depends on both the mass of an object and how that mass is distributed relative to the axis of rotation, whereas mass is a scalar quantity.
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, size, and the axis about which it rotates. Different shapes have different formulas for calculating moment of inertia.