A truck with 0.385 m radius tires travels at 44.5 m/s. At how many radians per second are the tires rotating?
v = omega R
omega = (44.5 m/s) / (.385 m)
To determine the number of radians per second the tires are rotating, we need to apply the formula:
angular velocity = linear velocity / radius of the tires.
First, convert the linear velocity from meters per second to radians per second. One revolution is equal to 2π radians, so:
44.5 m/s * (2π radians/1 revolution) = 44.5 * 2π radians/s
Next, divide the angular velocity by the radius of the tires:
angular velocity = 44.5 * 2π radians/s / 0.385 m
Calculating this expression gives the value of the angular velocity in radians per second.