Answer to Question #93524 in Classical Mechanics for alex

Question

Define an xy coordinate system on the face of an analog clock with the origin at the center. What is the horizontal component of a 3 cm long hour hand at 10:00 am?

Answer 1

Calculation of the angle between each hour.

$\theta_{div}=\frac{360^{0}}{12div}=30^{0}/div$

From the direction of the positive x-axis until 10am there are 5 divisions, therefore the degrees are

$\theta=5div*30^{0}/div=150^{0}$

Now, the horizontal component is given by

$cos\theta=\frac{r_{x}}{r}\\ r_{x}=r*cos\theta\\$

Numerically evaluating

$r_{x}=3.00cm*cos(150^{0})\\ r_{x}=-2.60cm$

The horizontal component of the long hand at 10:00am is

$\boxed{r_{x}=-2.60cm}$