1. What is Linear Acceleration in Curvilinear Motion?

Linear acceleration in curvilinear motion refers to the rate of change of linear velocity of an object moving along a curved path. It is directly related to the angular acceleration and the radius of the curved path.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a_{cm} \) — Linear acceleration (m/s²)
• \( \alpha_{cm} \) — Angular acceleration (rad/s²)
• \( r \) — Radius of the curved path (m)

Explanation: The linear acceleration of a point on a rotating object is equal to the product of the angular acceleration and the distance from the axis of rotation.

3. Importance of Linear Acceleration Calculation

Details: Calculating linear acceleration in curvilinear motion is essential for understanding the dynamics of rotating systems, designing mechanical components, and analyzing motion in circular paths.

4. Using the Calculator

Tips: Enter angular acceleration in rad/s² and radius in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between linear and angular acceleration?
A: Linear acceleration measures the rate of change of linear velocity, while angular acceleration measures the rate of change of angular velocity.

Q2: Can this formula be used for any curved path?
A: This formula specifically applies to circular motion where the radius is constant. For other curved paths, more complex calculations may be needed.

Q3: What are the units of measurement?
A: Angular acceleration is measured in radians per second squared (rad/s²), radius in meters (m), and linear acceleration in meters per second squared (m/s²).

Q4: How does radius affect linear acceleration?
A: For a given angular acceleration, linear acceleration increases proportionally with the radius. Points farther from the axis of rotation experience greater linear acceleration.

Q5: Is this formula valid for non-uniform circular motion?
A: Yes, this formula applies to both uniform and non-uniform circular motion, as it relates instantaneous angular acceleration to instantaneous linear acceleration.