You drive down the road at 39 m/s (88 mi/h) in a car whose tires have a radius of 34 cm.

What is the period of rotation of the tires?

(2 * π * 34 cm) / 39 m/s

watch your units

.06

To find the period of rotation of the tires, we need to calculate the time it takes for one complete revolution.

The formula to calculate the period of rotation (T) is:

T = circumference / linear velocity

First, let's convert the linear velocity from m/s to cm/s:

39 m/s * 100 cm/m = 3900 cm/s

The circumference of a circle (C) is calculated using the formula:

C = 2 * π * radius

So, let's calculate the circumference of the tires:

C = 2 * π * 34 cm ≈ 213.628 cm

Now, let's plug these values into the formula for the period of rotation:

T = 213.628 cm / 3900 cm/s ≈ 0.0549 s

Therefore, the period of rotation of the tires is approximately 0.0549 seconds.

To find the period of rotation of the tires, we need to know the angular speed of the tires, which can be calculated using the linear speed of the car and the radius of the tires.

The formula to calculate angular speed (ω) is:

ω = v / r

where v is the linear speed and r is the radius of the tires.

First, let's convert the linear speed from m/s to cm/s, since the radius is given in centimeters.

39 m/s × 100 cm/m = 3900 cm/s

Now, we can substitute the values into the formula:

ω = 3900 cm/s / 34 cm

Simplifying, we find:

ω ≈ 114.7 rad/s

The period (T) is the reciprocal of the angular speed:

T = 1 / ω

T ≈ 1 / 114.7 rad/s

Calculating this, we find:

T ≈ 0.0087 s

Therefore, the period of rotation of the tires is approximately 0.0087 seconds.