Question
A car tire can rotate at a frequency of 3000 revolutions per minute. Given that a typical tire radius is 0.5 m, what is the centripetal acceleration of the tire?
186
likes931 views
Answer to a math question A car tire can rotate at a frequency of 3000 revolutions per minute. Given that a typical tire radius is 0.5 m, what is the centripetal acceleration of the tire?
Hester
4.8116 Answers
To find the centripetal acceleration of the car tire, we can use the formula:
a = (v^2) / r
Where:
a is the centripetal acceleration,
v is the linear velocity of the tire, and
r is the radius of the tire.
First, we need to convert the frequency of 3000 revolutions per minute to linear velocity. Since each revolution covers the circumference of the tire, the linear velocity is given by:
v = 2ฯr * f
Where:
v is the linear velocity,
r is the radius of the tire, and
f is the frequency in revolutions per minute.
Substituting the values into the equation:
v = 2ฯ * 0.5 m * 3000 / 60
Simplifying:
v = ฯ * 0.5 m * 50
v = 25ฯ m/s
Now we can substitute the value of v into the centripetal acceleration formula:
a = (25ฯ m/s)^2 / 0.5 m
Simplifying:
a = (625ฯ^2) m^2/s^2
Therefore, the centripetal acceleration of the car tire is approximately 625ฯ^2 m^2/s^2.
625\pi^2\:\frac{m^2}{s^2}
Frequently asked questions (FAQs)
What is the product of a mixed number with 3 as its whole part, 1/2 as its fraction part and a real number 5, when factored?
+
What is the equation of the parabola that opens upward, has vertex (2,3), and passes through the point (4,11)?
+
What is the product of a mixed number, say 2 3/4, and a factored number, like 36, when multiplied by the square root of a real number, such as โ49?
+
New questions in Mathematics