I REALLY NEED HELP WITH THIS

Della Casee is riding a racing bike at a speed of 50.4 km/h. the wheels have a diameter of 70 cm. Find the angular velocity of the wheel in radians per second.

Convert the 50.4 km/h to cm/s.

Find the circumference of the 70cm diameter wheel.

Use the above values to find revolutions/second.
Multiply that by (2)(pi) to find radians/sec.

40 radians/second

40

Oh, well, it's time for a spin! Let's calculate that angular velocity with a dash of humor, shall we?

First, we need to convert that speed into meters per second because we don't want to confuse the poor wheel. So, 50.4 km/h translates to 14 meters per second. Now, buckle up!

To find the angular velocity, we need to know the circumference of the wheel. Luckily, the diameter is 70 cm, which means the radius (half the diameter, duh) is 35 cm or 0.35 meters.

The circumference of the wheel can be found by multiplying 2π (like a snatch of circus music) with the radius. So, 2π * 0.35 equals 2.2 meters.

Now, we divide the speed in meters per second (14) by the circumference (2.2). Excuse the wheel for a moment while it catches its breath.

The result is the number of rotations the wheel completes in one second. Since we're dealing with radians per second, and there are 2π radians in one rotation (cue the circus acrobats), we multiply the result by 2π.

So, 14 / 2.2 = 6.36 rotations per second. Multiply that by 2π (or one slip-up on a banana peel), and you get approximately 40 radians per second!

Voila! The angular velocity of the wheel is approximately 40 radians per second. Happy cycling, my friend!

To find the angular velocity of the wheel in radians per second, we need to convert the linear velocity (given in kilometers per hour) to angular velocity (in radians per second). Here's how you can do it:

Step 1: Convert the linear velocity from kilometers per hour to meters per second.
To convert kilometers per hour to meters per second, divide the speed by 3.6. In this case, we have:

50.4 km/h ÷ 3.6 = 14 m/s

Step 2: Calculate the circumference of the wheel.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, we need to find the radius of the wheel, which is half of the diameter.

Radius (r) = Diameter / 2 = 70 cm / 2 = 35 cm = 0.35 m

Therefore, the circumference (C) of the wheel is:

C = 2πr = 2π(0.35) = 2.2 m

Step 3: Calculate the angular velocity.
The angular velocity (ω) is given by the formula ω = v / r, where v is the linear velocity and r is the radius. Plugging in the values, we have:

ω = 14 m/s / 0.35 m ≈ 40 radians/s

So, the angular velocity of the wheel is approximately 40 radians per second.

09

144,000 rad/sec