Hi Katherine! To solve this problem, we will first convert the angular velocity from rev/sec to degrees/sec as shown below.
1 rev/sec * 360 deg/rev = 360 deg/sec
Next we will use this rate to find how long it will take the coin to rotate through 180 deg. To do this we will use unit analysis as shown below. Notice how the we use the reciprocal of the rate found above so that degrees divide out leaving seconds.
180 deg * (1 sec / 360 deg) = 0.5 sec
Next we are going to find how far it rolls in that amount of time. First we are going to find the circumference of coin (C) as shown below.
C = 2*pi*r = 2*3.14*10 = 62.8 mm
We know that every revolution the coin will travel a linear distance equal to its circumference. We are asked to find how far it travels when it rotates 180 deg or half a revolution. Therefore our answer is going to be half the circumference.
62.8/2 = 31.4 mm
I hope this helps! Please reach out if you have any follow up questions
