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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.

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