# Thread: Minute hand of a clock

1. ## Minute hand of a clock

The minute hand of a large clock is 6 feet long. Through what exact angle does the minute hand move in 30 minutes, and how far does the tip of the minute hand move in this time?

2. Originally Posted by christenc05
The minute hand of a large clock is 6 feet long. Through what exact angle does the minute hand move in 30 minutes, and how far does the tip of the minute hand move in this time?
The minute makes a complete rotation in an hour so it goes half in half an hour so the angle is $\pi$. The arc length is given by $r \theta$ where $r$ is the radius of the circular arc and $\theta$ is the angle suspending. In this case your arc length is $6 \times \ pi ft$.

Bobak

3. So does this mean that I just multiply 6 times `pi to get my answer. When I do this I get 18.84. Is this the angle or how far the tip of the minute hand has moved?

4. Originally Posted by christenc05
When I do this I get 18.84. Is this the angle or how far the tip of the minute hand has moved?
The hand goes halfway around the face in 30 minutes ( $\pi\text{ rad}$), and the length of the arc traced out by the tip of the minute hand is given by $s = r\theta = 6\pi$.