Remember, angular velocity is the angle by which an object turns in a certain time. Angular velocity can be expressed in degrees per unit time (second, minute, hour, etc.), radians per unit time, or even revolutions per unit time.
Let's practice with some simple examples again. We will begin with racing cars.
Examples:
1. A circle has 360 degrees, right? So an Indy car driver speeds through 360 degrees every time she makes a lap (we'll use a circular race track). If the racer makes 360 degrees (one loop) in one minute, how many degrees per second does she cover?
Solution
To find the rotation rate, or angular velocity, you will need to divide the number of degrees by the number of seconds in one minute. The answer is: (360 degrees) / (60 seconds) = 6 degree/second
2. This problem is not about cars, it is about planets. Assume that a planetary feature moves 36 degrees in 4 hours. Use the angular velocity to find how long it takes for that feature to go all the way around the planet.
Solution
Known turn = 36 degrees
Known time = 4 hours
Full rotation time = ?
Angular velocity = 36 degrees / 4 hours = 9 degree/hour
Full time rotation = 360 degrees / 9 degree/hour = 40 hours
With the invention of radar, the distance to Venus could be determined very precisely. By timing how long it takes the radar beam travelling at the speed of light to travel the distance to an object and back, the distance to the object can be found from distance = (speed of light) × (total time)/2. The total time is halved to get just the distance from the Earth to the object. Using trigonometry, astronomers now know that the astronomical unit =149,597,892 kilometers. This incredible degree of accuracy is possible because the speed of light is known very precisely and very accurate clocks are used. You cannot use radar to determine the distance to the Sun directly because the Sun has no solid surface to reflect the radar efficiently.