A car with 60 cm diameter tires is traveling at a constant speed of 100 km/hr. What is the angular velocity of the tires in rad/s?

r = .6/2 = .3 meters

v = w r = 100,000m/3600 s = 27.8 m/s
so'
w = 27.8/.3 = 92.6 radians/s

To find the angular velocity of the tires, we first need to convert the linear speed of the car into angular speed.

Angular speed is defined as the rate of change of angular displacement, and it is usually measured in radians per second (rad/s).

First, we need to convert the linear speed from km/hr to meters per second (m/s). We know that 1 km = 1000 m and 1 hr = 3600 s, so we can do the following conversion:

100 km/hr = (100 * 1000 m) / (3600 s) ≈ 27.78 m/s

Next, we need to find the circumference of the tires. Since the diameter of the tires is given as 60 cm, the radius would be half of that. So the radius of the tire is 60 cm / 2 = 30 cm = 0.3 m.

The circumference of a circle is given by the formula C = 2πr, where π (pi) is a constant approximately equal to 3.14159.

C = 2π * 0.3 m ≈ 1.88 m

Now we can calculate the angular speed:

Angular speed = Linear speed / Circumference.

Angular speed = 27.78 m/s / 1.88 m ≈ 14.78 rad/s.

Therefore, the angular velocity of the car's tires is approximately 14.78 rad/s.