Rotational Motion of speed and a car

[kalupahana]

Homework Statement

When a car is decelerating it's speed reduces from 80 km/h to 55 km/h. In this time the wheels of car complete 55 rotations. The diameter of the wheel is 1m.
Find the
1) angular acceleration of the car.
2) time taken to stop the car if it continued in same deceleration.

Homework Equations

v = rω
ω²₁ = ω²₀ + 2αθ
ω₁ = ω₀ + αt

Any equation regarding motion can be used to do this.
I used above three

The Attempt at a Solution

55 km/h = 15.2 m/s
80 km/h = 22.2 m/s

v = rω
I got ω = v/r from it. So
ω₀ = 22.2 m/s
ω₁ = 15.2 m/s

Then I used this equation to find angular acceleration
ω²₁ = ω²₀ + 2αθ

15.2² = 22.2² + 2 x 55 x π x α

-261.8 = 2 x 22/7 x 55 x α

α = -0.75 rad/s²

ω₁ = ω₀ + αt
can be use to find the time taken to stop

0 = 15.2 - 0.75t
t = 15.2/0.75 = 20.26 s


But in the textbook the answers are given as -1.5 rad/s² for angular acceleration and 20 sec for time taken to stop. But I got other things.
Please help me to complete this.
Thnx

 

[p21bass]

Assuming that they're actually asking for angular acceleration of each wheel, not the car - you seem to have erred in determining the angular displacement, as well as using the diameter of the wheel (instead of radius). Fixing those two errors gives the correct -1.5 rad/s^2 answer.

Your second part was done correctly, but you used the wrong values (found in the first part). Also - don't forget significant figures!

 

[kalupahana]

What should I take as Angular displacement.
It makes 55 rotations during that decelerating time. One rotation is 2П. Then 55 rotations means 110П rotations.
When I use like this i got 0.34 rad/s^2.

You said that second part is correct. But how.
I used the data gain by the first part.(The angular acceleration as 0.75).
If it was incorrect 20 sec could not be get.

The angular acceleration -1.5 rad/s^2 can be gain by 0.75 x 2. Please explain me how did you reached to the answer.

 

[p21bass]

110pi rotations is right. But, you it appears that you still haven't corrected your angular velocities by using radius, as opposed to diameter. Using the equations you posted as "Relevant Equations" gives you the right answers.

 

[kalupahana]

that means the radius is 1/2m.
Then velocities are come like 15.2 x 2 & 22.2 x 2.
Ok I understand. I'll try from it