An automobile tire has a radius of 0.380 m, and its center moves forward with a linear speed of v = 19.0 m/s.
(a) Determine the angular speed of the wheel. (Assume that there is no slipping of the surfaces in contact during the rolling motion.)
rad/s
(b) Relative to the axle, what is the tangential speed of a point located 0.175 m from the axle?
m/s I know this is 8.75 m/s
again I am able to answer the second part of the question,but no the first part. I get stuck on the first part.
To determine the angular speed of the wheel, we need to relate the linear speed of the tire's center to its angular speed. These two quantities are related by the formula:
v = ω * r
where:
- v is the linear speed of the tire's center (given as 19.0 m/s)
- ω (omega) is the angular speed of the wheel (unknown)
- r is the radius of the tire (given as 0.380 m)
To solve for ω, we rearrange the formula:
ω = v / r
Plugging in the given values:
ω = 19.0 m/s / 0.380 m
ω ≈ 50.0 rad/s
So the angular speed of the wheel is approximately 50.0 rad/s.
Note: Make sure to use consistent units when applying the formula. In this case, since both the linear speed and radius are given in meters, the resulting angular speed will be in radians per second.
If you have any further questions, feel free to ask!