Angular Speed Homework: Car Brakes, Radii & Revs

[mandy9008]

Homework Statement

A car initially traveling at 33.8 m/s undergoes a constant negative acceleration of magnitude 1.80 m/s2 after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330 m? (b) What is the angular speed of the wheels when the car has traveled half the total distance?

Homework Equations

v² = v_o² + 2aΔx
C=2πr

The Attempt at a Solution

a. Δx = v_o² /-2a
Δx = 33.8 m/s ² / (-2(-1.80 m/s²))
Δx = 317.3 m

# rev = 317.3 m / 2π (0.33m)
# rev = 153.1

b. v² = 33.8 m/s² + 2(-1.80 m/s²)(158.65m)
v = 23.9 m/s --> ω = 23.9 rad/s

 

[dulrich]

Everything is fine except the very last step. The tangential velocity of the wheel is related to the angular velocity via v_T = rω. The reason you can assume that v = v_T is because the wheels do not skid.