Question on circular motion, finding out the angular displacement in a clock.

[mutineer123]

Homework Statement

A clock is showing 3.30. Calculate the angular displacement in degrees from the 12.00 position of the clock to:
i the minute hand
ii the hour hand

I got my minute answer as 180 degree, which is right. But my second answer was 90 degrees, which apparently is wrong! the answer theyr giving is 105 degrees! how come? even just looking at the hour hand, we can see that the angular displacement should be 90 degrees! they did something like 3.5/12 X 360 degrees.

Homework Equations

The Attempt at a Solution

 

[Jimmy]

When the clock reads 3:30, is the hour hand pointing directly at 3 or is it somewhere between 3 and 4?

 

[mutineer123]

When the clock reads 3:30, is the hour hand pointing directly at 3 or is it somewhere between 3 and 4?

holy crap, u are right. Its btween 3 and 4...I totally overlooked that!

 

[Jimmy]

It's a bit of a trick question. My first reaction was that the answer is wrong until I thought about it for a few seconds.

 

[Nickie]

The angular displacement of the hour hand can be calculated by taking the fraction of time passed in hours (3.5/12) and multiplying it by the total degrees in a full circle (360 degrees). This gives us 105 degrees, which is the correct answer.

The reason for this is that the hour hand moves at a slower rate than the minute hand. In order to reach the 3.30 position, the hour hand has to travel 3.5 hours (since it is closer to the 4 o'clock mark than the 3 o'clock mark). This means that the hour hand has moved more than just 90 degrees from the 12.00 position.

To better understand this, imagine if the clock only had an hour hand and the time was 3.30. In this case, the hour hand would be pointed directly at the 3 o'clock mark, indicating an angular displacement of 90 degrees from the 12.00 position. However, since there is also a minute hand on the clock, the hour hand has to move further to reach the 3.30 position, resulting in an angular displacement of 105 degrees.

It is important to consider the difference in rates at which the hour hand and minute hand move when calculating angular displacement in a clock. This is because the minute hand moves at a constant rate of 6 degrees per minute, while the hour hand moves at a rate of 30 degrees per hour. Therefore, the angular displacement of the hour hand will always be larger than that of the minute hand when measuring from the 12.00 position.