# Moment of inertia + torque

## 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
Homework Helper
Your calculation appease to be correct.

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

use conservation of energy.

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
Homework Helper
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.

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

i've got

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

180/pi x 0.1724 = 9.91 degrees?

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.

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:

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

i've got

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

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.

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

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

1/2x1.1x10-4x602=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.

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

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

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

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!

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