Radians and Clock physics question-behind in class and need help

Question

What is the angular position in radians of the minute hand of a clock at 1:15?

Answer 1

To find the angular position in radians of the minute hand of a clock at 1:15, you can use the following approach:

1. First, note that a clock has 12 hours, and the minute hand makes a full rotation (360 degrees or 2π radians) around the clock face in one hour (60 minutes).

2. At 1:15, the minute hand has moved 15 minutes past the 12 o'clock position. To find the angular position in radians, you can use the proportion:

Angular position in radians = (Minutes past 12 o'clock / 60) * 2π

In this case:

Angular position in radians = (15 minutes / 60 minutes) * 2π

Angular position in radians = (1/4) * 2π

Now, calculate the angular position:

Angular position in radians = (1/4) * 2π = 1/2 * π = π/2 radians

So, at 1:15, the minute hand of the clock is at an angular position of π/2 radians from the 12 o'clock position.