# Rotation of a wheel question

1. Jul 6, 2004

### winterma

Hi, I have a few questions, thanks for any help you can give!!!!

1. If a wheel is rotating at a rate of 3.1 revolutions every 3.6 seconds. Through what angle, in radians, does the wheel rotate in 1 second??

2. A car can negotiate an unbanked curve safely at a certain maximum speed when the coefficient of static friction between the tires and the ground is 0.85. At what angle should the same curve be banked for the car to negotiate the curve safely at the same maximum speed without relying on friction?

3. A 0.073 kg arrow is fired horizontally. The bowstring exerts an average force of 60N on the arrow over a distance of 0.78m. With what speed does the arrow leave the bow? (for this one, i used the formula 1/2mv^2, but did not get the correct answer, maybe i'm using the incorrect formula)

Thanks!

2. Jul 6, 2004

### AKG

You can figure these out yourself with a little help.

There is an equation very similar to the equation that relates constant speed, time, and distance travelled to an equation that relates similar concepts, but their rotational analogues. You know the equation:

$$v = \frac{\Delta d}{\Delta t}$$

where $v$ is the constant speed, $\Delta d$ is the distance travelled, and $\Delta t$ is the time elapsed. Now, let $\Delta \theta$ represent the angle through which an object has gone, and $\omega$ the constant angular velocity. There is a formula, then, as follows:

$$\omega = \frac{\Delta \theta}{\Delta t}$$

Coefficient of static friction? I don't exactly understand what it means to bank a curve at a certain angle.

Why did you use that formula? Do you know what that formula is for? Can you show your work? What is the book's given answer?