6.2 Centripetal Acceleration

6.2 Centripetal Acceleration

  • If an earth mover with larger tires was moving at the same speed, its tires would spin more slowly.
  • Both are linear and have directions.
    • The axis of rotation can be either clockwise or counterclockwise.
  • Tie an object to the end of a string and swing it around in a horizontal circle above your head.
    • To calculate the linear speed at this point, you need to identify a point close to your hand.
  • Measure the angular velocities of other circular motions.
  • A fly on the edge of an old fashioned vinyl record is always connected to the circle.
    • The direction of the velocity is not straight.
  • The ladybug is exploring rotational motion.
    • The merry-go-round can be rotating to change its angle.
    • Circular motion relates to the bug's x,y position, velocity, and acceleration.
  • We know that the change in velocity is either in its magnitude or in its direction.
    • Even though the magnitude of the velocity might be constant, there is always an associated acceleration in uniform circular motion.
    • When you turn a corner in your car, you experience this acceleration of your own.
    • You can see that the car is changing direction.
    • The sharper the curve, the more noticeable it will be.
    • The direction and magnitude of that acceleration is examined in this section.
  • An object is moving in a circular path.
    • Two points along the path are shown the direction of the instantaneous velocity.
    • The center of the circular path is the direction of the change in velocity.
    • The diagram in the figure shows this pointing.
  • The directions of the velocity of an object at two different points are shown, and the change in velocity is seen to point towards the center of curvature.
    • centripetal acceleration is when the acceleration is also toward the center.
  • The triangle formed by the velocities and the ones formed by the radii are similar.
    • There are two equal sides to the ABC and PQR triangles.
    • The two sides of the triangle have the same speeds.
  • 6.16 is the acceleration of an object in a circle.
    • When driving a car, centripetal acceleration is greater at high speeds and in sharp curves.
    • It's a bit surprising that it's four times harder to take a curve at 100 km/h than it is at 50 km/h.
    • You have probably noticed that a sharp corner has a larger radius for tighter turns.
  • It's useful to express in terms of speed.
    • We find substituting into the above expression.
  • The direction of travel is towards the center.
    • You can use whichever expression is more convenient.
  • The time it takes for separation to occur is greatly reduced by high centripetal acceleration.
  • In science and medicine, centrifugations are used to separate single cell suspensions from a liquid medium and to separate macromolecules from a solution.
    • Centrifuges are often rated in terms of their centripetal acceleration relative to gravity, and the maximum centripetal acceleration of several hundred thousand is possible in a vacuum.
    • The tolerance of astronauts to the effects of accelerations larger than Earth's gravity has been tested with Human Centrifuges.
  • The curve taken at highway speed is fairly gentle due to gravity.
  • The most convenient expression to use is the first one.
  • The ratio is used to compare this with the acceleration due to gravity.
    • It's noticeable if you weren't wearing a seat belt.
  • If it were to continue in a straight line, it would have to be accelerated.
  • Determine the ratio of the acceleration to the gravity.
  • The term is used for revolutions per minute.
    • The angular velocity is obtained by converting this to radians per second.
  • The second expression in the equation can be used to calculate the centripetal acceleration.
  • We use the facts that one revolution is and one minute is 60.0 s to convert to radians per second.