Angular motion of a car wheel traveling at certain speed

[inuka00123]

Homework Statement

a car is travelling at certain speed, wheels are circling 7 rounds per second, after some time it accelerates in 5 second to twice the speed before, how much angular displacement the wheel has during 5 seconds of acceleration

Relevant Equations

ω = θ/t, α = ω/t

I assumed first the car is travelling 7 rad/s then accelerated to 14 rad/s in 5 seconds, after plugging the variables, I got θ = 35, I must be wrong about this calculation, can someone explain, if wrong give me the way of calculation please?

 

[BvU]

7 rounds per second means seven revolutions, not seven radians ...

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[inuka00123]

yeah, I saw that it means I need to multiply it by 2pi to get to the radians, can you give me the answer for this question, it would help me to compare my solution and what is correct to find what I am missing more

7 rounds per second means seven revolutions, not seven radians ...

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[jbriggs444]

I assumed first the car is travelling 7 rad/s then accelerated to 14 rad/s in 5 seconds, after plugging the variables, I got θ = 35,

Can you show your work for this? Just giving us the final answer will not tell us where you went wrong.

If the wheels are turning at 7 rad/s and keep turning for 5 seconds then even without any acceleration they will rotate through 35 radians in 5 seconds.

So you need to add in the acceleration somehow. There are a couple of ways to think about doing that. One way would be to get the average rotation rate.

 

[BvU]

yeah, I saw that it means I need to multiply it by 2pi to get to the radians, can you give me the answer for this question, it would help me to compare my solution and what is correct to find what I am missing more

You will need another relevant equation. Can you show it ?

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[inuka00123]

Can you show your work for this? Just giving us the final answer will not tell us where you went wrong.

If the wheels are turning at 7 rad/s and keep turning for 5 seconds then even without any acceleration they will rotate through 35 radians in 5 seconds.

So you need to add in the acceleration somehow. There are a couple of ways to think about doing that. One way would be to get the average rotation rate.

I am sorry, but as BvU stated it is not 7rad/s but 7 revolutions and 14 revolutions. the question I asked is wrong

 

[inuka00123]

Can you show your work for this? Just giving us the final answer will not tell us where you went wrong.

If the wheels are turning at 7 rad/s and keep turning for 5 seconds then even without any acceleration they will rotate through 35 radians in 5 seconds.

So you need to add in the acceleration somehow. There are a couple of ways to think about doing that. One way would be to get the average rotation rate.

is it wrong to just use the θ = revolutions per second x 2π, after plugging the equations,

θ₁ = rev x 2π
= 7 x 2π
= 44 radians

θ₂ = rev x 2π
= 14 x 2π
= 88 radians

*to get the θ between acceleration I subtract θ₁ from θ₂, and got 44 radians. when the acceleration come into this equation, I do not understand.

 

[kuruman]

is it wrong to just use the θ = revolutions per second x 2π, after plugging the equations,

θ₁ = rev x 2π
= 7 x 2π
= 44 radians

θ₂ = rev x 2π
= 14 x 2π
= 88 radians

*to get the θ between acceleration I subtract θ₁ from θ₂, and got 44 radians. when the acceleration come into this equation, I do not understand.π

This post shows that you are confused. You are given an initial angular speed of 7 revolutions per second. This means that if this number does not change, for every second that goes by, the wheel makes 7 revolutions or turns by an angle of 7×2π = 14π radians. However, here the wheel is speeding up because after 5 seconds have gone by, we are told that the speed has doubled. If the speed changes, the wheel is accelerating.

Can you find the acceleration given that the angular speed increases from 7 revolutions per second to 14 revolutions per second?
If so, were you taught the kinematic equations relating acceleration and displacement?

 

[jbriggs444]

Can you find the acceleration given that the angular speed increases from 7 revolutions per second to 14 revolutions per second?

Or, another approach, can you (@inuka00123) find the average angular speed over the interval?

 

[inuka00123]

I am really confused, if I find the acceleration using ω₁ = ω₀ + at equation and plug that onto another equation or I can just use the θ = 1/2 (ω₁ + ω₀)t equation, right?, my textbook is really confusing, and 1/2 (ω₁ + ω₀) would be the average speed, or avg angular velocity, or angular speed I suppose

 

[kuruman]

I am really confused, if I find the acceleration using ω₁ = ω₀ + at equation and plug that onto another equation or I can just use the θ = 1/2 (ω₁ + ω₀)t equation, right?, my textbook is really confusing, and 1/2 (ω₁ + ω₀) would be the average speed, or avg angular velocity, or angular speed I suppose

Either way you will get the same answer if you do it right. Using the average angular velocity as @jbriggs444 suggested is more straightforward. Try it that way, get a number and post your solution. Then try it the other way using the acceleration. If the numbers are the same, you will have learned something and perhaps be less confused.

 

[inuka00123]

I tried different equations, every one seems give a = 8.8 rad/s² and for displacement 330 radians, because I tried to plug the answer to different equations and got the same solution, I think it is correct, thank you!

 

[kuruman]

I agree with your numbers.