A truck with 0.100 m radius tires travels at 24.0 m/s. At how many radians per second are the tires rotating? What is this in rpm?
Circumference = pi * 2r =
3.14 * 0.20 = 0.6283 m/rev.
Va = 24m/s * 6.28rad/0.6283m = 240 rad/s
= Angular velocity.
V = 24m/s * 1rev/0.6283m * 60s/min =
2292 RPM.
To determine the number of radians per second that the tires are rotating, we can use the formula:
angular velocity (in radians per second) = linear velocity / radius
Given that the radius of the tires is 0.100 m and the truck is traveling at 24.0 m/s, we can substitute these values into the formula:
angular velocity = 24.0 m/s / 0.100 m
angular velocity = 240 radians/second
Therefore, the tires are rotating at 240 radians per second.
To convert this angular velocity to RPM (Revolutions Per Minute), we need to know the relation between radians and revolutions.
1 revolution = 2π radians
To convert from radians per second to revolutions per minute, we can use the following conversions:
1 revolution per minute = 2π radians per second
So, to convert 240 radians per second to revolutions per minute, we can calculate:
angular velocity (in RPM) = 240 radians/second * (1 revolution / 2π radians) * (60 seconds / 1 minute)
angular velocity (in RPM) ≈ 2290 RPM
Therefore, the tires are rotating at approximately 2290 RPM.