AN AUTOMOBILE TIRE HAS A RADIUS OF 0.330M AND ITS CENTER MOVES FORWARD WITH A LINEAR SPEED OF V= 15.0M/S. a) DETERMINE THE ANGULAR SPEED OF THE WHEEL. B) RELATIVE TO THE AXLE, WHAT IS THE TANGENTIAL SPEED OF A POINT LOCATED 0.175M FROM THE AXLE?
omega = v/r = 15/.33 radians/second
.175 * omega
A) Ah, the "wheel" of fortune! To find the angular speed of the wheel, we can use the formula:
Angular speed (ω) = Linear speed (v) / Radius (r)
Plugging in the values we have, ω = 15.0 m/s / 0.330 m. Crunching the numbers, the angular speed of the wheel is approximately 45.45 rad/s.
B) The ax-lie in this equation is that you want to know the tangential speed of a point located 0.175 m from the axle. To find this, we can use the equation:
Tangential speed = Angular speed × Radius
Plugging in the values, the tangential speed is equal to 45.45 rad/s × 0.175 m, which gives us approximately 7.96 m/s.
So, the point located 0.175 m from the axle is moving at a speed of approximately 7.96 m/s. Zoom, zoom!
a) To determine the angular speed of the wheel, we can use the relationship between linear speed and angular speed, which is given by:
v = ω * r
where v is the linear speed, ω is the angular speed, and r is the radius of the tire.
In this case, we are given the linear speed v = 15.0 m/s and the radius r = 0.330 m. Plugging these values into the formula, we can solve for the angular speed ω:
15.0 m/s = ω * 0.330 m
To solve for ω, we can divide both sides of the equation by 0.330 m:
ω = 15.0 m/s / 0.330 m
ω ≈ 45.45 rad/s
Therefore, the angular speed of the wheel is approximately 45.45 rad/s.
b) To determine the tangential speed of a point located 0.175 m from the axle, we can use the relationship between tangential speed and angular speed, which is given by:
vt = ω * rt
where vt is the tangential speed, ω is the angular speed, and rt is the radius of the point from the axle.
In this case, we are given the angular speed ω ≈ 45.45 rad/s and the radius from the axle rt = 0.175 m. Plugging these values into the formula, we can solve for the tangential speed vt:
vt = 45.45 rad/s * 0.175 m
vt ≈ 7.96 m/s
Therefore, the tangential speed of a point located 0.175 m from the axle is approximately 7.96 m/s.
To solve this problem, we need to use the relationship between linear speed, angular speed, and radius. Here's how we can find the answers to both parts of the question:
a) Determining the angular speed of the wheel:
We know that linear speed (v) is equal to the product of the angular speed (ω) and the radius (r) of the tire. Mathematically, it can be represented as:
v = ω * r
To find the angular speed (ω), we rearrange the formula:
ω = v / r
Substituting the given values, we get:
ω = 15.0 m/s / 0.330 m
ω ≈ 45.45 rad/s
Therefore, the angular speed of the wheel is approximately 45.45 rad/s.
b) Determining the tangential speed of a point located 0.175 m from the axle, relative to the axle:
The tangential speed of a point on the wheel can be found using the formula:
Tangential Speed = Angular Speed * Radius
Substituting the known values, we get:
Tangential Speed = 45.45 rad/s * 0.175 m
Tangential Speed ≈ 7.97 m/s
Therefore, the tangential speed of a point located 0.175 m from the axle, relative to the axle, is approximately 7.97 m/s.