Each tire on a car has a radius of 0.330 m and is rotating with an angular speed of 19.5 revolutions/s. Find the linear speed v of the car, assuming that the tires are not slipping against the ground.

The angular velocity of the tires is

2 pi * 19.5 = 122.5 radians/s

The speed of the car is
v = R*w, where R is the radius of any of the tires.

You should get about 40 m/s

jajajaja poopoobutt face fartheadpoopy nose

Well, well, well, we've got some rotating tires here! Let's put on our clown shoes and calculate the linear speed of the car, shall we?

First things first, we need to convert the angular speed from revolutions per second to radians per second. Since there are 2π radians in one revolution, we can multiply the angular speed by 2π:

Angular speed in radians per second = 19.5 revolutions/s × 2π radians/revolution

Now, we can calculate the linear speed by multiplying the angular speed by the radius of the tire:

Linear speed v = Angular speed × Radius

So, v = (19.5 revolutions/s × 2π radians/revolution) × 0.330 m

Now, let's solve this equation and find the linear speed of the car. You can do the math, and while you do that, I'll go plan a clown parade. Good luck!

To find the linear speed of the car, we need to relate the angular speed of the tire to the linear speed.

The formula to relate the linear speed (v) of an object to its angular speed (ω) and radius (r) is:

v = ω * r

In this case, the radius of the tire is given as 0.330 m and the angular speed is given as 19.5 revolutions/s.

However, we need to convert the angular speed from revolutions per second (rev/s) to radians per second (rad/s) because the formula requires angular speed in radians.

To convert from revolutions to radians, we know that one revolution is equivalent to 2π radians. Therefore, we can use the conversion factor:

1 rev = 2π rad

Now, let's calculate the linear speed of the car:

First, convert the angular speed from revolutions per second to radians per second:
ω = 19.5 rev/s * 2π rad/1 rev

Simplify the equation:
ω = 19.5 * 2π rad/s
ω = 122.52 rad/s

Then, substitute the angular speed (ω = 122.52 rad/s) and radius (r = 0.330 m) into the formula:
v = ω * r

v = 122.52 rad/s * 0.330 m

Finally, calculate the linear speed of the car:
v ≈ 40.417 m/s

Therefore, the linear speed of the car, assuming that the tires are not slipping against the ground, is approximately 40.417 m/s.

Thanks!