# Angular Acceleration Homework: Find Car Wheel Speed Change

• LBenson
In summary, the problem involves a car with 0.6m diameter wheels accelerating from 3m/s to 18m/s in 10 seconds. To find the angular acceleration, the equation A=v-u/t can be used after converting the linear speeds to angular velocities. The solution is 5rad/s^2. To find the number of revolutions made by each wheel during the speed change, the equation θ = (ω2 + ω1) t/2 can be used after finding the angular velocities. The solution is 55.7 revolutions.
LBenson

## Homework Statement

A motor car with wheels of 0.6,m diameter accelerates uniformly from 3 to 18m/s in 10 seconds.

Find:

a) the angular acceleration of the wheels
b) the number of revolutions made by each wheel during the speed change

## Homework Equations

A=v-u/t (angular equivilent with Alpha as acceleration etcetc)

## The Attempt at a Solution

My first thought was to change the 3m/s and 18m/s into Rad/s but I'm unsure how to go about doing that.

Then using A=v-u/t i assume the acceleration can be found

I have no clue how to attempt the second part.

Cheers.

You can relate the linear speed and acceleration with the rotational values by realizing that the tires should be in contact with the ground the whole time, and so any distance covered by the vehicle will be equal to the arc length that the wheels have rotated by.
Similarly any acceleration in the vehicle will correspond to an "acceleration" (or change) of the arc length.
If s=arc length r=radius and θ=the angle rotated
then use the relation:
s=rθ

Sorry, I'm a tad lost over this whole situation...

I really have no clue where to start

I think, you should consider an equation that show relationship between velocity and angular velocity. Then derive it and from here you can find angular acceleration.

Ok i think i got it.

After looking back through my notes i found V=wr (W being angular velocity)

I rearranged for w (w=v/r) and worked out the angular velocity for both the 3m/s and the 18m/s

So w1=3/0.3 (since 0.6 was the diameter 0.3 = radius) = 10rad/s

Then
A=w2-w1/t

Which is the right answer since i have the marks scheme infront of me.

Now just to crack on with the next part. Cheers for the help.

ApexOfDE said:
I think, you should consider an equation that show relationship between velocity and angular velocity. Then derive it and from here you can find angular acceleration.

Should have refreshed my page a few minutes earlier :)

Thanks for the help.

If you're curious i got the second part by using θ = (ω2 + ω1) t/2

So
θ = (60 + 10) 10/2
Needed in revs so to convert:
350/2pi = 55.7revs

## 1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is a measure of how fast an object is rotating or changing its direction of rotation.

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

Angular acceleration is a measure of the change in rotational motion, while linear acceleration is a measure of the change in linear motion. Angular acceleration is expressed in radians per second squared, while linear acceleration is expressed in meters per second squared.

## 3. How do I calculate angular acceleration?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula is: a = (ω₂ - ω₁) / (t₂ - t₁), where a is the angular acceleration, ω is the angular velocity, and t is the time.

## 4. What is the relationship between angular acceleration and tangential acceleration?

Tangential acceleration is a type of linear acceleration that is directed tangent to the circular path of an object. The magnitude of tangential acceleration is equal to the radius of the circular path multiplied by the angular acceleration. In other words, the greater the angular acceleration, the greater the tangential acceleration.

## 5. How can I use angular acceleration to find the change in car wheel speed?

By knowing the angular acceleration of the car's wheels and the initial speed, you can use the formula v = ωr to calculate the final speed, where v is the linear speed, ω is the angular velocity, and r is the radius of the wheel. Then, you can calculate the change in wheel speed by subtracting the initial speed from the final speed.

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