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?

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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 = 2πr * 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 = 2π * 0.5 m * 3000 / 60
Simplifying:
v = π * 0.5 m * 50
v = 25π m/s
Now we can substitute the value of v into the centripetal acceleration formula:
a = (25π m/s)^2 / 0.5 m
Simplifying:
a = (625π^2) m^2/s^2
Therefore, the centripetal acceleration of the car tire is approximately 625π^2 m^2/s^2.
625\pi^2\:\frac{m^2}{s^2}

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