Angular Positions of a clock
1) What is the angular position in radians of the minute hand of a clock at 5:00?
To start this problem, you have to pay close attention to what they are asking: “the minute hand”.
It is assumed that from 9 to 3 on the clock would make a 180 ° angle.
The minute hands points at the “12″ at 5:00. The minute hand pointing at “12″ yields 90 °relative to the previously establish model of 180 °.
We know the angular position of the minute hand at 5:00 is 90 °. All we have to do is convert degrees to radians. To do this:
We multiply the degrees by π/180
90 × π/180= 90π/180
90π/180 = 1.57 rad or radians
θ =1.57 rad
2) What is the angular position in radians of the minute hand of a clock at 6:15?
Since the minute hand is on 3 the angle is zero.
0 × π/180= 0π/180
0/180 = 0 rad or radians
θ =0 rad
3) What is the angular position in radians of the minute hand of a clock at 2:55?
This problem is a little trickier because the angle is not as clear cut as the other ones. To find the angle, we just need to do a little thinking. A whole circle is 360 °. There are 12 numbers in an analog clock. If you divide 360 by 12, you would get 30. Each number would represent 30°. At 2:55, the minute hand would stop at “11″. This is basically 90 ° with an added 30 degrees, which would equal to 120 °.
120 × π/180= 120π/180
376.99/180 = 2.09 rad or radians
θ =2.09 rad