A car traveling 50 m/s has tires tires that with radii of 0.25 m. The driver of the car hits the brakes and brings the car to a stop in 5 seconds. What is the angular acceleration of the tires on the car?

a = (0-50) / 5 = -10m/s^2.

C = pi*D = 3.14 * (2*0.25) = 1.57m/rev.

V=10m/S^2 * (1/1.57)rev/m * 6.28rad/rev
= 40rad/s^2.

To find the angular acceleration of the car's tires, we can use the formula:

α = ωf - ωi / t

where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time taken.

To compute the angular acceleration, we need to calculate the initial and final angular velocities.

The linear velocity of the car is given as 50 m/s. The linear velocity of a point on the edge of a rotating object is related to the angular velocity by the equation:

v = r * ω

where v is the linear velocity, r is the radius, and ω is the angular velocity.

Rearranging the equation to solve for ω, we have:

ω = v / r

Plugging in the values, we get:

ω = 50 m/s / 0.25 m
ω = 200 rad/s

Therefore, the initial angular velocity of the car's tires is 200 rad/s.

The final angular velocity is zero since the car comes to a stop. So, ωf = 0 rad/s.

Substituting the values in the formula for angular acceleration, we get:

α = 0 - 200 rad/s / 5 s
α = -40 rad/s^2

Hence, the angular acceleration of the car's tires is -40 rad/s^2. The negative sign indicates that the tires are decelerating or slowing down.