What is linear speed and angular speed
(In Trignometry)
linear speed is speed along a given path, normally a straight line.
angular speed is some changing angle that changes as a function of time. The change in angle per unit time is angular speed. For instance, if a car wheel makes a complete rotation in 10 seconds, its angular speed is 360deg/10 sec or 36 deg/sec. Normally, in physical science, we use radians/sec as a standard unit for angular speed.
In motion around a circle, angular speed is related to tangential speed
angular speed in rad/sec= tangential speed/ radius
if i have something in revolutions per sec what is that(a.s. or l.s.) and how would I convert that to miles per hour
how do linear speed and angular speed relate
Unless you know the radius of curvature, it is apples and oranges.
radiusofCurvature*angularspeedINRev/sec*2Pi rad/rev= tangential speed in unit of radiius/sec.
then convert that to mph
we learned it using the formula:
theta = s/r
can you explain how the formulas for both of these equations relate to their definition
In trigonometry, linear speed and angular speed are concepts used to describe the motion of an object.
1. Linear Speed:
Linear speed refers to how fast an object is moving in a straight line or along a curved path. It is typically measured in units such as meters per second, miles per hour, or kilometers per hour.
To calculate linear speed, you need to know the distance traveled and the time taken. The formula can be expressed as:
Linear Speed = Distance / Time
For example, if an object travels a distance of 100 meters in 10 seconds, the linear speed would be:
Linear Speed = 100 meters / 10 seconds = 10 meters per second
2. Angular Speed:
Angular speed, on the other hand, refers to the rate at which an object rotates or moves in a circular path. It is usually measured in units such as radians per second or degrees per second.
To calculate angular speed, you need to know the angle rotated and the time taken. The formula can be expressed as:
Angular Speed = Angle / Time
However, it is important to note that the angle is typically measured in radians when using trigonometry. If the angle is given in degrees, it has to be converted to radians using the conversion factor:
1 radian = 180 degrees / π
For example, if an object rotates through an angle of 1.5 radians in 2 seconds, the angular speed would be:
Angular Speed = 1.5 radians / 2 seconds = 0.75 radians per second
So, linear speed deals with straight-line or curved motion, while angular speed deals with rotational or circular motion.