The speedometer on an automobile measures the rotational speed of the axle and converts that to a linear speed of the car, assuming the car has 0.62-m-diameter tires.
What is the rotational speed of the axle when the car is traveling at 26m/s ?
To find the rotational speed of the axle when the car is traveling at 26 m/s, we can use the formula that relates linear speed and rotational speed.
The formula is:
v = ω * r
Where:
v is the linear speed (in m/s)
ω (omega) is the rotational speed (in rad/s)
r is the radius of the tires (in meters)
Given information:
v = 26 m/s (linear speed)
r = 0.62 m (radius)
To find ω, rearrange the equation:
ω = v / r
Plugging in the values:
ω = 26 m/s / 0.62 m
Calculate the value of ω:
ω ≈ 41.94 rad/s
Therefore, the rotational speed of the axle when the car is traveling at 26 m/s is approximately 41.94 rad/s.