6.1 Rotation Angle and Angular Velocity

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.