# Angular Velocity and Acceleration

• df102015
In summary, the car is traveling at 27.8 m/s and undergoes a negative acceleration of 2.6 m/s/s when the brakes are applied. The wheels each have a radius of 1.0 m. To find the number of revolutions the tires will go through before the car comes to a stop, we use the formula ω = v / r to find the angular velocity of the wheels, which is 27.8. Then, using the formula Θ = ω t + 0.5 α t^2, we can solve for the angular displacement of the wheels, which is 297.46°. Since the car is coming to a stop, we can assume that the angular

## 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.

df102015 said:
ω = Θ / t
27.8 = Θ / 10.7
Θ = 297.46°
Careful. ω is not a constant.

df102015 said:
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?

Doc Al said:
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?

haruspex said:
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?

df102015 said:
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.

df102015 said:
the angular velocity of the wheel?
As Doc Al posted, that is not constant here. So the angular velocity when?

haruspex said:
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?

df102015 said:
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.

df102015 said:
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?

SteamKing said:
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?
df102015 said:
ω = v / r
ω = 27.8 / 1
ω = 27

## 1. What is angular velocity?

Angular velocity is the rate at which an object rotates or changes its angular position over time. It is measured in radians per second (rad/s) in the SI system.

## 2. How is angular velocity different from linear velocity?

Angular velocity is a measure of rotational motion, while linear velocity is a measure of straight-line motion. Angular velocity is expressed in terms of angle per unit time, while linear velocity is expressed in terms of distance per unit time.

## 3. What is the relationship between angular velocity and angular acceleration?

Angular velocity and angular acceleration are related in the same way that linear velocity and linear acceleration are related. Angular acceleration is the rate at which angular velocity changes over time, similar to how linear acceleration is the rate at which linear velocity changes over time.

## 4. How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. It is expressed in radians per second squared (rad/s²) in the SI system.

## 5. What factors can affect angular velocity and acceleration?

The main factors that can affect angular velocity and acceleration are the shape and mass distribution of the rotating object, as well as any external forces or torques acting on the object. Friction, air resistance, and gravity can also play a role in determining angular velocity and acceleration.