The outer edge of a truck tire that has a radius of 25 cm has a velocity of 26 m/s. What is the angular velocity of the tire in rad/s?
http://www.jiskha.com/display.cgi?id=1290754007
C = 6.28*r = 6.28 * 25 cm = 157 cm = 1.57 m.
V = 26 m/s * 1/1.57 rev/m * 6.28 rad/rev = 104 rad/s.
The linear velocity of a point on the outer edge of a rotating object is related to its angular velocity and the radius by the formula:
v = ω * r
Where:
v is the linear velocity
ω (omega) is the angular velocity
r is the radius
To find the angular velocity (ω), we can rearrange the formula as:
ω = v / r
Given that the linear velocity (v) is 26 m/s and the radius (r) is 25 cm (0.25 m), we can substitute these values into the formula:
ω = 26 m/s / 0.25 m
Simplifying the expression:
ω = 104 rad/s
Therefore, the angular velocity of the truck tire is 104 rad/s.
To find the angular velocity of the tire in rad/s, you need to use the formula:
Angular velocity (ω) = Velocity (v) / Radius (r)
Given:
Velocity (v) = 26 m/s
Radius (r) = 25 cm
First, convert the radius from centimeters to meters:
Radius (r) = 25 cm = 0.25 m
Now substitute the values into the formula:
Angular velocity (ω) = 26 m/s / 0.25 m
Divide 26 by 0.25 to get the angular velocity:
Angular velocity (ω) = 104 rad/s
Therefore, the angular velocity of the truck tire is 104 rad/s.