# Angular Velocity and Acceleration

## Homework Statement

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?

## Homework 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

## 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.

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Doc Al
Mentor
ω = Θ / t
27.8 = Θ / 10.7
Θ = 297.46°
Careful. ω is not a constant.

haruspex
Homework Helper
Gold Member
2020 Award
ω = Θ / t
What, exactly, does dividing an angular displacement by an elapsed time give you? Yes, it's an angular velocity, but what angular velocity?

Careful. ω is not a constant.
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?

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

haruspex
Homework Helper
Gold Member
2020 Award
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?
I assume you are familiar withthe SUVAT equations for linear motion at constant acceleration. It's just the same for angular motion.

haruspex
Homework Helper
Gold Member
2020 Award
the angular velocity of the wheel?
As Doc Al posted, that is not constant here. So the angular velocity when?

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

haruspex
Homework Helper
Gold Member
2020 Award
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?
Yes.

SteamKing
Staff Emeritus
Homework Helper
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?
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?

haruspex