# Angular Velocity and Acceleration

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1. Apr 13, 2016

### df102015

1. The problem statement, all variables and given/known data
A car is traveling at 27.8 m/s, it undergoes a negative acceleration of 2.6 m/s/s when the brakes are applied. How many revolutions will the tires go through before the car comes to a stop if the wheels each have a radius of 1.0 m?

2. Relevant equations
α = at / r -> angular acceleration = tangential acceleration / radius
α = ω / t -> angular acceleration = angular velocity / time
α = Θ / t^2 -> angular acceleration = angle / time^2
ω =
Θ / t -> angular velocity = angle / time
ω = v / r -> angular velocity = velocity / radius

3. The attempt at a solution
ω = v / r
ω = 27.8 / 1
ω = 27.8

α = a / r
α = (- 2.6) / 1
α = -2.6

α = ω / t
-2.6 = 27.8 / t
27.8 / 2.6 = t
10.7sec = t

ω = Θ / t
27.8 = Θ / 10.7
Θ = 297.46°

297.46 / 360 = 0.83 times

This was incorrect.

2. Apr 13, 2016

### Staff: Mentor

Careful. ω is not a constant.

3. Apr 13, 2016

### haruspex

What, exactly, does dividing an angular displacement by an elapsed time give you? Yes, it's an angular velocity, but what angular velocity?

4. Apr 13, 2016

### df102015

i'm not sure what you mean by that... are you saying that ω is not 27.8 ?
How would i solve for ω the correct way?

5. Apr 13, 2016

### df102015

the angular velocity of the wheel?

6. Apr 13, 2016

### haruspex

I assume you are familiar withthe SUVAT equations for linear motion at constant acceleration. It's just the same for angular motion.

7. Apr 13, 2016

### haruspex

As Doc Al posted, that is not constant here. So the angular velocity when?

8. Apr 13, 2016

### df102015

Yes and so would i use Θ = ω t + 0.5 α t^2 ?
and ω would be the angular velocity of the wheel before deceleration?

9. Apr 13, 2016

### haruspex

Yes.

10. Apr 13, 2016

### SteamKing

Staff Emeritus
You're given the linear velocity of the car before deceleration and the radius of the wheels. Don't you think that there is some formula which can relate these two pieces of information?

11. Apr 13, 2016