Angular acceleration of tires on a car

[Spartan301]

Homework Statement

You accelerate your car from rest at a constant rate down a straight road and reach 22.0 m/s in 111s. The tires on your car have radius 0.320 m. Assuming the tires rotate in a counterclockwise direction, what is the angular acceleration of the tires?

Homework Equations

Givens:
Initial velocity: 0
Final velocity: 22.0 m/s
Elapsed time: 111s
Tire radius: 0.320 m

Objective: Find the angular acceleration of the tires.

Battle Plan:
Find the linear displacement from the average acceleration and the elapsed time.
(vf² = vi² + 2aΔx)
Find the circumference of the tires from the radius, and divide the linear displacement by the circumference to find the number of rotations in that length.
Use ΔΘ = Θf-Θi, having multiplied the number of full rotations by 2π.
Divide the angular displacement by the elapsed time to find angular velocity.
Divide the change in angular velocity by the elapsed time to find angular acceleration

The Attempt at a Solution

Outcome:
a = 0.198198198
vf² = vi² + 2aΔx
vf² - vi² = 2aΔx
(vf² - vi²)/2a = Δx
22 m²/s² / 2(0.198198198 m/s^2) = Δx
22 m²/s² / 0.396396396 m/s^2
Linear displacement: 55.5 m

Radius: 0.320 m
Circumference = 2π(0.320m) = 2.010619298 m

55.5 m/ 2.010619298 m = 27.60343544 rotations.

27.60343544 rotations x 2π = 173.4375 radians

173.4375 radians/ 111s = 1.5625 rad/s

1.5625 rad/s / 111s = 0.014076577 rad/s²

They say the answer is supposed to be 0.619 rad/s²

Thank you for your help. Let me know if I can return the favor.

-Tom

 

[tiny-tim]

Hi Tom!

linear displacement = r x angular displacement: s = rθ

linear speed = r x angular speed: v = rω

linear acceleration = r x angular acceleration: a = rα

 

[Spartan301]

Thanks for replying Tim.

Hi Tom!

linear displacement = r x angular displacement: s = rθ

linear speed = r x angular speed: v = rω

linear acceleration = r x angular acceleration: a = rα

I do not understand.

 

[tiny-tim]

The tires on your car have radius 0.320 m … what is the angular acceleration of the tires?
…
a = 0.198198198
…
They say the answer is supposed to be 0.619 rad/s²

a = rα

 

[Spartan301]

Ooooh! Now I understand! Good job! Thank you!