Shortcut Methods and Tricks for Vector Products- Angular Velocity and Angular Acceleration

1. Linear Velocity:

• Shortcut: Linear velocity (v) = Angular velocity (ω) × Radius (r).
• Trick: Remember the formula v = rω as a simple multiplication of angular velocity and radius.

2. Angular Acceleration:

• Shortcut: Angular acceleration (α) = (Final angular velocity (ωf) - Initial angular velocity (ωi)) / Time (t).
• Trick: Use the formula α = (ωf - ωi)/t to quickly calculate angular acceleration from given angular velocity changes over time.

3. Centripetal Force:

• Shortcut: Centripetal force (F) = Mass (m) × (Linear velocity)²/Radius (v² / r)
• Trick: Remember the formula F = mv²/r as the square of linear velocity divided by radius.

4. Number of Revolutions:

• Shortcut: Number of revolutions (N) = (Initial angular velocity (ωi) × Time (t)) / (2 × π).
• Tips: Use the formula N = (ωi × t)/(2π) to calculate the number of revolutions made before stopping.

5. Quick Conversions:

• To convert from RPM (revolutions per minute) to rad/s (radians per second): Multiply the RPM value by 2π/60.

Examples:

• 1000 RPM = (1000 × 2π/60) rad/s ≈ 104.72 rad/s

• To convert from rad/s to RPM: Multiply the rad/s value by 60/2π.

Examples:

• 20 rad/s = (20 × 60/2π) RPM ≈ 191.94 RPM

These shortcuts and tricks will help you solve numericals related to vector products, angular velocity, and angular acceleration more efficiently and accurately.