Leon’s bicycle wheels have a circumference of 2 m. What is his linear speed when the wheels rotate at 1 revolution per second? Show all work leading to your answer.

The wheel doesn't slip on the ground so the ground goes by at the same rate that a point on the rim of the wheel moves.
1 revolution per second= 1 circumferences per second= 2 meters per second
2(meters/sec)* (3600sex/hr)* (1km/1000m)
= 7.2 km per hr.

v = ω * r

where
v = linear/tangential velocity (m/s)
ω = angular velocity (rad/s)
r = radius (m)

Since the wheels rotate at 1 rev/s (this is the angular velocity), its equivalent to rad units is 2π rad/s.
And since the wheels have circumference of 2 m, the radius is
C = 2πr
r = 2/(2π)
r = 1/π meters
Substituting,
v = (2π rad/s) * (1 / π meters)
v = 2 m/s
If you want to convert it in km/hr,
2 m/s * (1 km / 1000 m) * (3600 s / hr) = 7.2 km/hr

Your answer is correct. :)
hope this helps~ `u`

Thank you :)

To find Leon's linear speed when the wheels rotate at 1 revolution per second, we can start by calculating the distance traveled in one revolution using the circumference formula.

Circumference = π * diameter

Since we are given the circumference of the wheels, we can calculate the diameter by dividing the circumference by π:

Diameter = Circumference / π = 2 m / π

Next, we need to find the distance traveled in one second when the wheels rotate at 1 revolution per second. Since the circumference is the distance traveled in one revolution, the distance traveled in one second is equal to the circumference:

Distance traveled in 1 second = Circumference = 2 m

Finally, to convert the linear speed from meters per second to kilometers per hour, we can use the conversion factor:

1 km = 1000 m
1 hour = 3600 seconds

Linear speed in km per hour = (Distance traveled in 1 second * 3600) / 1000

Substituting the values:

Linear speed = (2 * 3600) / 1000 = 7200 / 1000 = 7.2 km per hour

Therefore, Leon's linear speed when the wheels rotate at 1 revolution per second is 7.2 km per hour.

To calculate Leon's linear speed, we can use the formula:

Linear Speed = Circumference * Rotational Speed

Given that the circumference of Leon's bicycle wheels is 2 meters and the wheels rotate at 1 revolution per second, we can substitute these values into the formula:

Linear Speed = 2 meters * 1 revolution per second

Since 1 revolution is equal to the circumference of the wheel, which is 2 meters, the calculation simplifies to:

Linear Speed = 2 meters per second

So, Leon's linear speed is 2 meters per second.

If we want to convert this speed to kilometers per hour, we can multiply the linear speed by the following conversion factors:

2 meters per second * (3600 seconds per hour) * (1 kilometer per 1000 meters)

By simplifying the units, we get:

2 meters per second * 3600 seconds per hour * 1 kilometer per 1000 meters

Which equals:

7.2 kilometers per hour

Therefore, Leon's linear speed, when the wheels rotate at 1 revolution per second, is 7.2 kilometers per hour.