Moment of inertia + torque

[ar202]

Homework Statement

A vehicle wheel has a mass 2.5 kg and diameter 310 mm. The vehicle moves from rest to a linear velocity of 13 kmh -1 in 60 s. Assuming that the wheel can be treated as a solid disc, find the torque applied to the wheel

Homework Equations

Not so sure on how to add equations that aren't basic...

The Attempt at a Solution

I started with

0.5 x 2.5 x 0.155² = 0.3003125

then

3.61ms-1 / 0.155 = 23.29 rads-1

23.29-0/60=0.388172043 (angular acceleration)

so then it should be

0.388172043 x 0.3003125 = 0.1165729167 Nm right?

 

[rl.bhat]

Your calculation appease to be correct.

 

[ar202]

i'm on my last question, i'll put it here instead of starting numerous threads... :uhh:

A hollow cylinder of mass 50 g and external and internal diameters of 50 mm and 44 mm respectively, rolls down a slope for a distance of 5 m without slipping. If the cylinder starts from rest and has a velocity of 3 ms-1 by the time it reaches the 5m point, what was the angle of incline of the slope

i'm a bit lost on where to start... i know it's something to do with potential energy...

btw thanks for looking at the other one

 

[benhou]

use conservation of energy.

 

[ar202]

use conservation of energy.

ke = pe ?

h = 1/2 x 3²/9.81 ?

can i then assume it's a right angle triangle? or am i off target...?

 

[rl.bhat]

Initial velocity, final velocity and displacement of the cm of the cylinder is given. Find the acceleration of the center of mass.
The equation of motion for translation a nd for rotation about the axis through cm is
ΣFx = Mg*sinθ + (-f) = M*a(cm) ....(1)
Στ = f*R = Iα = I*R*a(cm) .......(2) where f is the frictional force.
Substitute the value of I in the eq.2 and find the expression for a(cm). From that find θ.

 

[ar202]

ok went over some notes... was getting carried away

i've got

0.05x9.81x5Sinθ=0.225+0.198 (all sources of ke)

sinθ=0.1724 radians right?

180/pi x 0.1724 = 9.91 degrees?

 

[benhou]

ke = pe ?

h = 1/2 x 3²/9.81 ?

can i then assume it's a right angle triangle? or am i off target...?

Well, what is its total kinetic energy? By the way, it would be helpful if you shown all your work. I was a little lost for a few minutes.

 

[ar202]

Well, what is its total kinetic energy? By the way, it would be helpful if you shown all your work. I was a little lost for a few minutes.

yes apologies!! bit lazy of me :tongue2:

 

[benhou]

ok went over some notes... was getting carried away

i've got

0.05x9.81x5Sinθ=0.225+0.198 (all sources of ke)

sinθ=0.1724 radians right?

180/pi x 0.1724 = 9.91 degrees?

ok, so you used conservation of energy instead of forces. But could you explain how you got "0.225+0.198 (all sources of ke)". It seems too small for me.

 

[benhou]

Never mind, I got it. It's the mass 0.05.
It looks good now.

 

[ar202]

ok, so you used conservation of energy instead of forces. But could you explain how you got "0.225+0.198 (all sources of ke)". It seems too small for me.

1/2x0.05x3²=0.225

1/2x1.1_x10-4x60²=0.198

i've done 3/0.05=60 rads-1 used the radius of the first diameter, no idea if this is correct or not or whether there is a way of using them both.

 

[benhou]

I believe 1.1*10⁴ is the moment of inertia, could you show me how you did it as well.

 

[ar202]

ok cool, cheers. does my answer seem ok in your opinion?

having an open-book test in a couple of days thought i would do as many examples as possible for reference.

 

[ar202]

I believe 1.1*10⁴ is the moment of inertia, could you show me how you did it as well.

moment of inertia for a hollow disc = 1/2xm(r1^2+r2^2) if that makes sense. sorry i'm not familiar with how to add fancy text for formulas

 

[benhou]

It's ok for now, but it would be really helpful if you did know. Here's how to learn latex code:
https://www.physicsforums.com/misc/howtolatex.pdf

moment of inertia for a hollow disc = 1/2xm(r1^2+r2^2) if that makes sense. sorry i'm not familiar with how to add fancy text for formulas"

I thought the + should be -. But ya, you are right. Good luck with your review!

 

[ar202]

Is it possible to work out an objects angular velocity when you're only give it's moment of inertia, mass and radius...?