Centripetal Accelaration

• What is centripetal acceleration defined as?

  The acceleration towards the center of a circle

  
• How is centripetal acceleration related to an object's motion?

  It occurs when an object rotates at constant speed
• What variables are used in the centripetal acceleration formula?

  a, v, r
• What does the variable 'a' represent in the centripetal acceleration formula?

  Centripetal acceleration in m/s²
• What does the variable 'v' represent in the centripetal acceleration formula?

  Linear speed in m/s
• What does the variable 'r' represent in the centripetal acceleration formula?

  Radius of the circular orbit in meters
• How is linear speed 'v' related to angular speed 'ω'?


  v = rω
• What does the equation for centripetal acceleration show when combined with angular speed?

  Centripetal acceleration equals radius times angular speed squared

  
• What is the direction of centripetal acceleration?

  Toward the center of the circle

  
• How does centripetal acceleration relate to an object's velocity?

  It is perpendicular to the object's velocity
• If the radius is doubled and angular speed is doubled, how do you calculate centripetal acceleration?

  Use the formula with new values
• What happens to centripetal acceleration if both radius and angular speed are doubled?

  It increases by a factor of four
• What are the key equations for centripetal acceleration?

  1. \( a = \frac{v^2}{r} \)
  2. \( v = r\omega \)
  3. \( a = r\omega^2 \)
• What are the relationships between centripetal acceleration, linear speed, and angular speed?

  • Centripetal acceleration is proportional to the square of linear speed.
  • Centripetal acceleration is proportional to the radius and the square of angular speed.
  • Centripetal acceleration is always directed towards the center of the circle.