To solve this problem, we need to first determine the angular velocity of the tires when the car starts to brake. We can use the formula:
ω = ω0 + αt
Where:
ω = angular velocity (final)
ω0 = initial angular velocity (when the car starts to brake)
α = angular acceleration
t = time
Since the car tires are initially spinning at a constant speed, the initial angular velocity is simply the linear velocity divided by the tire radius:
ω0 = v / r
Plugging in the values:
ω0 = 20 m/s / 0.33 m = 60.606 rad/s
Next, we'll use the formula for angular velocity to calculate the time it takes for the tires to stop spinning:
0 = ω0 + αt
Rearranging the equation:
t = (-ω0) / α
Plugging in the values:
t = (-60.606 rad/s) / (40 rad/s^2)
t = -1.515 s
Since time cannot be negative, we'll take the positive value:
t = 1.515 s
Therefore, it takes approximately 1.515 seconds for the car tires to stop spinning.
You are travelling forward in a car at 20 m/s. Your car tires have a radius of 33 cm. You slam on the brakes, which slows the tires at an angular acceleration of 40 rad/s^2.
How long until the tires are no longer spinning (although the car may still be sliding forward) in s?
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