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