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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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