Question

A point starts at the location (−4,0)and moves CCW along a circle centered at (0,0) at a constant angular speed of 2 radians per second. Let t represent the number of seconds since the point has swept out since it started moving. Draw a diagram of this to make sure you understand the context!Suppose the point has traveled for 0.25 seconds (t=0.25). How many radians would need to be swept out from the 3-o'clock position [or from (4,0)] to get to the point's current position?_______ radians   Write an expression in terms of t to represent how many radians would need to be swept out from the 3-o'clock position to get to the point's current position.

Answer 1

In this problem we have a circle centered at origin with radius 4 units

we have an angular speed of 2 radians per second

step 1

Find out the circumference of the circle

$C=2\pi r$

we have

r=4

substitute

$\begin{gathered} C=2\pi(4) \\ C=8\pi\text{ units} \end{gathered}$

the length of the circumference subtends a central angle of 2pi radians

we have 2 radians per second

If the point has traveled for 0.25 seconds and the angular speed is 2 radians per second

that means

has traveled 0.25*2=0.50 radians

the distance between point (-4,0) and (4,0) is pi radians

the point need

(pi-0.50) radians