Rotating bodies, Car around a corner

[Sakura22]

Homework Statement

A car turns a corner with a radius of curvature of 11.1 m while braking to reduce its speed. If the brakes generate an angular deceleration of 0.5 rad/s2 what is the magnitude of the acceleration of the car half way through the corner when the car's linear speed is 9.6 m/s?

Homework Equations

Tangential velocity= wr
arc lenth=r(theta)
equation: w^2=(w0)^2 + 2 (angular acceleration)(theta)

The Attempt at a Solution

What I did was I converted the linear speed into angular speed by using the first formula, then I found the time, and halved it, but the answer I'm getting for acceleration HALF WAY is not correct, I have no clue what I did wrong.
Please help

Homework Statement

A square sheet with a uniform density and total mass m is pivoted about an axis A in one corner of the sheet and perpendicular to the plane of the sheet as shown below. If the moment of inertia of the sheet about this axis is \frac{8}{3}ma^2, what is the sheet's moment of inertia about a parallel axis, B, at the mid-point of one of its sides?

http://moodle.phys.uAlberta.ca/file.php/2/questions/images/rotation/rotation-parallelaxis.png

 

[Delphi51]

Welcome to PF, Sakura.
I can't tell what you did wrong - you haven't shown your work!

 

[Sakura22]

Welcome to PF, Sakura.
I can't tell what you did wrong - you haven't shown your work!

Hey! Sorry about that..but here it goes..
a(tangential) = wr
= 11.1m x 0.5 rad/s^2
=5.55 m/s^2
Then I used the formula
v=v0 + at
v= at
v= 5.55 m/s^2 x t
t= 9.6 m/s^2 / 5.55 m/s^2
t= 1.73
t/2 because it asks for the deceleration half way through the curve
Then I used the v=at again with half the time = 0.865 ..
then v=at
a=v/t --> 9.6 m/s / 0.865 seconds
= 11.098 m/s^2

Please tell me what I did wrong..thanks again for your help.

 

[Sakura22]

For the 2nd question I have no clue, so please give some hints, so I can get something going in my head.

 

[Doc Al]

a(tangential) = wr
= 11.1m x 0.5 rad/s^2
=5.55 m/s^2

You found the tangential component of the acceleration. So far, so good!

Then I used the formula
v=v0 + at
v= at
v= 5.55 m/s^2 x t
t= 9.6 m/s^2 / 5.55 m/s^2
t= 1.73
t/2 because it asks for the deceleration half way through the curve
Then I used the v=at again with half the time = 0.865 ..
then v=at
a=v/t --> 9.6 m/s / 0.865 seconds
= 11.098 m/s^2

Not sure what you're doing here. You need the radial component of the acceleration. Note that they tell you the speed, so no need for any kinematics. (Hint: The motion is circular.)

 

[Sakura22]

What is the radial component? I don't understand. Is that the centripetal acceleration?

 

[Doc Al]

Is that the centripetal acceleration?

Eactly! (The "radial" direction is along the radius, thus perpendicular to the tangential direction.)

 

[Sakura22]

Eactly! (The "radial" direction is along the radius, thus perpendicular to the tangential direction.)

I am not sure about the formula BUT..here is what I think should work..please tell me if its correct a(centripetal)= w^2 r

 

[Sakura22]

Also, please give me some hints about the second problem, thanks

 

[Doc Al]

I am not sure about the formula BUT..here is what I think should work..please tell me if its correct a(centripetal)= w^2 r

That's perfectly correct. You can also use a different formula for centripetal acceleration (equivalent of course) expressed in terms of tangential speed v, instead of ω.

 

[Doc Al]

A square sheet with a uniform density and total mass m is pivoted about an axis A in one corner of the sheet and perpendicular to the plane of the sheet as shown below. If the moment of inertia of the sheet about this axis is \frac{8}{3}ma^2, what is the sheet's moment of inertia about a parallel axis, B, at the mid-point of one of its sides?

http://moodle.phys.uAlberta.ca/file.php/2/questions/images/rotation/rotation-parallelaxis.png

The diagram is not viewable. Hint: Make use of the parallel axis theorem.

Try posting the diagram to a publically accessible image hosting site.

 

[Sakura22]

http://moodle.phys.uAlberta.ca/file.php/2/questions/images/rotation/rotation-parallelaxis.png

 

[Sakura22]

I missed the class on The parallel axis theorem, and now I looked it on the wikipedia website, I don't understand it.

 

[Doc Al]

I missed the class on The parallel axis theorem, and now I looked it on the wikipedia website, I don't understand it.

Your textbook should describe it. Also read this: http://hyperphysics.phy-astr.gsu.edu/hbase/parax.html"