# Friction and Rolling of a disk

## Homework Statement

Disk a and b are identical and roll across a floor with equal speeds. Disk a rolls up an incline, reaching a max height h, and disk B moves up an incline that is identical except that it is frctionless. Is the max height reached by disk b greater than, less than, or equal to h?

## Homework Equations

Conservation of Energy

## The Attempt at a Solution

Both disks have the same initial kinetic energies. When they go up the ramp, wouldn't friction oppose the way of motion for the wheels? I don't understand how friction would help the wheel move up higher.

I also thought that energy of disk a would be spent in heat from the friction too, making it have a max height less than that of disk b.

The answer is that disk b reaches a max height less than that of disk a

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SammyS
Staff Emeritus
Homework Helper
Gold Member
Take a vertical disk that's rotating:

Set it down on a frictionless surface. What happens? It keeps rotating but doesn't move.

Set it down on a surface with some friction. What happens? It starts rolling & its rate of rotation decreases.

ehild
Homework Helper
There is static friction when the disk rolls. Static friction do not cause loss of mechanical energy, but it means torque that changes angular speed. When the disk rolls upward, the speed of its CM is equal to the angular speed times the radius. When the kinetic energy decreases with height, both the angular speed and the translational speed decrease.
Without friction, there is no torque so the angular speed does not change. The rotational energy stays the same. When the disk does not travel further, it is still rotating. So it reaches lower height.

ehild

So, the ball won't go up the frictionless ramp. In a way, friction pushes the ball up then. How can this be explained with conservation of energy? Shouldn't the ball have more energy if it went up a frictionless ramp?

What does Cm stand for?

ehild
Homework Helper
Center of mass

ehild

tiny-tim
Homework Helper
hi joej24!
So, the ball won't go up the frictionless ramp.
no, it will

friction on rolling things is needed to accelerate them …

friction is not needed to keep them at the same speed

a car moving at 30 mph and going onto a patch of ice will stay at 30 mph …

if it meets a hill of ice, it will move up the hill exactly as if it had no wheels and was just sliding on its chassis …

if the ice ran out half-way up the hill, the car would keep going, but the wheels would start to take up some of the energy …

basically this whole problem is about how much of the energy goes into the linear motion of the disc, and how much into the rotational motion

btw, note the careful wording of the question …
Disk a rolls up an incline, reaching a max height h, and disk B moves up an incline that is identical except that it is frctionless​
… A rolls, but B "moves" (ie, doesn't roll)!

The ball loses a lot more energy while rolling up a frictionless ramp, than when it actually rolls up a ramp.
If you use the equation mgh=1/2mv2+1/2I(omega)2 where I equals the moment of inertia of the ball and omega equals (v2/r2)

and if you use just mgh=1/2mv2, the ball that is rolling has its rotational inertia, so It will roll further up the ramp than the ball that just slides.

tiny-tim
Homework Helper
Yes, if there's no friction, the ball will still be spinning when it reaches maximum height,

but if there is friction, the the ball will be stationary when it reaches maximum height, so more kinetic energy will have been lost by the ball, and so it will have more potential energy (ie height).

So the friction makes the ball lose angular speed. Eventually, the ball will stop spinning. No torque is acted upon the ball going up the frictionless ramp, so it keeps on spinning. So since more kinetic energy is used up by the one going to ramp with friction, the more energy is converted to potential energy (higher height). And since the other ball keeps its rotational kinetic energy, less energy was converted to potential then.

Is this right?

ehild
Homework Helper
Yes.

ehild