Angular acceleration - Please check if this is correct and

[nukeman]

Angular acceleration - Please check if this is correct and...

Homework Statement

Question:

Each of the tires of a car makes 85.0 revolutions as the car reduces its speed uniformly from 90.0 km/h to 60.0 km/m, The tires have a diamater of .900m.

Find initial and final angular Velocities

Find the angular acceleration of tires in rad/s^2

My answers: Please tell me if that's right, because I have NO idea if its correct.

Homework Equations

The Attempt at a Solution

 

[grzz]

If I am interpreting your work correctly, you are changing the km to m by multiplying by 900 instead of by 1000.

I think that the rest is OK.

 

[nukeman]

Oops lol

Where wherever I have 900, change to 1000 correct? Just to be sure :)

Because when I change that, I get -1.60 is that correct for this question?

Because someone told me they got -4.88 ?

 

[grzz]

I got angular acc = -1.605rad/sec^2.

 

[asteriatic]

Your answers are partially correct. The initial and final angular velocities should be in units of radians per second (rad/s), not revolutions per second (rev/s). To convert from revolutions to radians, you can use the conversion factor 1 revolution = 2π radians. So the initial angular velocity would be (85.0 rev)*(2π rad/rev) = 170π rad/s.

The final angular velocity can be found using the formula ωf = ωi + αt, where ωi is the initial angular velocity, α is the angular acceleration, and t is the time interval. Since the car is reducing its speed from 90.0 km/h to 60.0 km/h, the time interval would be the difference in time between these two speeds. You can use the formula d = vt to find the time interval, where d is the distance traveled (which is equal to the circumference of the tire), v is the velocity, and t is the time. So the final angular velocity would be ωf = 170π rad/s + αt.

To find the angular acceleration, you can use the formula α = (ωf - ωi)/t, where ωf and ωi are the final and initial angular velocities, respectively, and t is the time interval. You can use the same time interval that you found for the final angular velocity.

So to summarize, your answers should be:

Initial angular velocity: 170π rad/s
Final angular velocity: 170π rad/s + αt
Angular acceleration: α = (ωf - ωi)/t