10.2 Kinematics of Rotational Motion

10.2 Kinematics of Rotational Motion

  • Estimate the magnitudes of the quantities.
  • There is both magnitude and direction in the acceleration.
  • The most common units of the magnitude of the acceleration are.
    • The direction of linear acceleration along a fixed axis is marked by a + or a - sign, just as the direction of linear acceleration in oneDIMENSION is marked by a + or a - sign.
  • A gymnast is doing a forward flip.
    • The mat would be parallel to her left.
    • Her moment of inertia about her spin axis would affect the magnitude of her acceleration.
  • 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.
  • By using our intuition, we can see how rotational quantities are related to one another.
    • If a motorcycle wheel has a large angular acceleration for a long time, it ends up spinning rapidly and rotating through many revolutions.
    • If the wheel's speed is large for a long period of time, the final speed and angle of rotation are large.
    • The motorcycle's large final velocity and large distance traveled are similar to the wheel's rotational motion.
  • The description of motion is called keematics.
    • Let's find an equation relating,, and.
  • The symbol will be used for linear or tangential acceleration from now on.
    • We assume is constant, which means that angular acceleration is also a constant.
  • The last equation describes their relationship without reference to forces or mass that may affect rotation.
    • It's similar in form to its counterpart.
  • Kinematics for rotational motion is very similar to.
    • The description of motion without regard to force or mass is called keematics.
  • The equations given in Table 10.2 can be used to solve a constant problem.
  • Examine the situation to find out if rotational motion is involved.
    • Without the need to consider forces that affect the motion, rotation must be involved.
  • Identifying the unknowns will help determine exactly what needs to be determined in the problem.
    • A sketch of the situation is useful.
  • A list of what can be inferred from the problem can be made.
  • The quantity to be determined is determined by the appropriate equation or equations.
    • It is useful to think in terms of a translation because you are familiar with it.
  • To get numerical solutions complete with units, substitute the known values along with their units into the equation.
    • Units of radians are used for angles.
  • A deep-sea fisherman hooks a big fish that swims away from the boat and pulls the fishing line from his reel.
    • The entire system is at rest and the fishing line can be pulled from the reel at a distance of 3.50 cm from the axis of rotation.
  • The same strategy was used for each part of the example.
    • A relationship is sought that can be used to solve for unknown values.
  • The easiest equation to use is because the unknown is already on one side and all other terms are known.
  • radians must always be used in calculation of linear and angular quantities.
    • radians are not dimensions.
  • We are asked to find the number of revolutions.
    • We can find the number of revolutions by looking at radians.
  • This example shows that the relationships among rotational quantities are very similar to those among linear quantities.
  • This example shows how linear and rotational quantities are connected.
    • The answers to the questions are correct.
    • After two seconds, the reel is found to spin at 220 rad/s.
    • When the big fish bites, the amount of fishing line played out is 9.90 m.
  • Fishing line coming off a rotating reel moves linearly.

If the fisherman applies a brake to the spinning reel, what happens?

  • The reel needs time to stop.
    • The initial and final conditions are different from the previous one.
    • The initial and final velocities are zero.
    • The acceleration is given to be.
    • The easiest way to use this equation is by seeing all the quantities but t.
  • Care must be taken with the signs that show the directions.
    • The time to stop the reel is small because the acceleration is large.
    • Fishing lines sometimes snap because of the accelerations involved, and fishermen often let the fish swim for a while before applying brakes on the reel.
    • A tired fish needs a smaller acceleration.
  • The freight trains accelerate slowly.
    • Imagine a train that goes from rest to full speed, giving its wheels an acceleration of.
  • We are asked to find in part and in part.
    • The number of revolutions, the radius of the wheels, and the angular acceleration are given to us.
  • The equation would have at least two unknown values, so we can't use it.
  • The distance traveled is large and the final speed is slow.
  • The following example shows that there is motion for something spinning in place.
    • The total distance is calculated using the example below.
  • The plate is shown in the image.
    • The food is heated while the fly makes revolutions.