Set 9 Problem number 3

• Problem

• Solution

• Generalized Solution

• Explanation in terms of Figure(s), Extension

• Figure(s)

Problem

An object moves at constant angular velocity around a circle of radius 4.6 meters, making a revolution every 8.1 seconds. 

• If the angular position of the object is 0 radians t = 0 seconds, what are the x and y coordinates of the object's position after t seconds?

Solution

Moving through a revolution, which is 2 `pi radians, in 5 seconds, the object will have an angular velocity of

`omega = 2 `pi radians/( 8.1 seconds) = .7757 radians/second.

After t seconds, starting at 0 radians when t = 0, the angular position will be

theta = ( .7757 radians/second ) (t seconds) = .7757 * t radians.

Its x and y coordinates are therefore

x1 = 4.6 meters * cos ( .7757 t)

and

y = 4.6 meters * sin( .7757 t).