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6.1 Rotation Angle and Angular Velocity

- The arcs of a bird's flight and Earth's path around the Sun are examples of curved motions.
- If there is a net external force, motion is along a straight line at constant speed.
- We will study the forces that cause motion along curves.
- This chapter is a continuation of Dynamics:Newton's Laws of Motion as we study more applications of the laws of motion.

- The study of this topic will lead to the study of many new topics under the name rotation.
- When points in an object move in circular paths, it's called pure rotational motion.
- The motion is motion with no rotation.
- There is a rotating hockey puck moving along ice.

- We studied motion along a straight line and introduced concepts such as displacement, velocity, and acceleration.
- Projectile motion is a case in which an object is projected into the air while being subject to the force of gravity.
- In this chapter, we look at situations where the object does not land but moves in a curve.
- The study of uniform circular motion begins by defining two quantities.

- There is a line from the center of the CD to the edge.
- The amount of rotation is similar to linear distance.

- There is a rotation of the circle's radius.
- The length is described.

- The length of the circle is known as the arcs length.
- The circle's diameter is.

- Table 6.1 shows a comparison of radians and degrees.

- Points 1 and 2 are the same angle, but point 2 is at a greater distance from the center of rotation.

- If rad, the CD has made one complete revolution, and every point on the CD is back at its original position.

- The greater the rotation angle, the greater the velocity.
- The units are radians per second.

- The velocity is similar to the linear one.
- The pit on the rotating CD is used to get the precise relationship between the two variables.

- The largest point on the rim is proportional to the distance from the center of rotation.
- The linear speed of a point on the rim is called the tangential speed.
- Consider the tire of a moving car as an example of the second relationship in play.
- The speed of a point on the rim of a tire is the same as the speed of a car.
- The tire spins large if the car moves fast.
- A larger-radius tire will produce a greater linear speed for the car.

- The tire rotation is the same as if the car were jacked up.
- The tire radius is where the car moves forward at linear velocity.
- A larger tire's speed is related to the car's speed.

- When the car travels at about, calculate the car tire's angular velocity.

- We can use the second relationship in to calculate the angular velocity if we know the tire's radius.

- We get 50.0/s when we cancel units.
- The units of rad/s must be in the angular velocity.

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