1. What is Tangential Velocity?

Tangential velocity is the linear speed of an object moving along a circular path. It's always tangent to the circle at any given point and represents how fast the object is moving along the circular path.

2. How Does the Calculator Work?

The calculator uses the tangential velocity formula:

Where:

• \( v \) — Tangential velocity (m/s)
• \( \omega \) — Angular velocity (rad/s)
• \( r \) — Radius of the circular path (m)

Explanation: The tangential velocity is directly proportional to both the angular velocity and the radius of rotation.

3. Importance of Tangential Velocity

Details: Tangential velocity is crucial in understanding circular motion, rotational dynamics, and applications like centrifuges, planetary motion, and rotating machinery.

4. Using the Calculator

Tips: Enter angular velocity in radians per second (rad/s) and radius in meters (m). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How is tangential velocity different from angular velocity?
A: Angular velocity measures how fast the angle changes (rad/s), while tangential velocity measures the actual linear speed along the circular path (m/s).

Q2: Can tangential velocity be constant while angular velocity changes?
A: Yes, if the radius changes inversely proportional to the angular velocity (v = ωr remains constant).

Q3: What's the relationship between tangential velocity and centripetal acceleration?
A: Centripetal acceleration (a) is related to tangential velocity by a = v²/r.

Q4: How do you convert RPM to rad/s for ω?
A: Multiply RPM by 2π/60 (1 RPM = 0.10472 rad/s).

Q5: Does tangential velocity depend on mass?
A: No, tangential velocity depends only on angular velocity and radius, not on the mass of the object.