Calculate Friction Required for Rolling Without Slipping (Down a Hill) | Force

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Calculate the required coefficient of static friction required for an object to roll down a hill without slipping.
The coefficient of friction must be adequate to cause a rotational acceleration that is consistent with the translational acceleration of the wheel.
This solution works for any round shape of object so long as it has a consistent radius and a known moment of rotational inertia.
This problem comes up in introductory physics courses including AP Physics 1, AP Physics C Mechanics and appears on the JEE as well as A Level Physics Exam.

[@jacobgalinski2948]

No idea how your channel isn’t more popular, your videos explain things excellently in a very efficient manner.
Seriously thanks for all the help

[@INTEGRALPHYSICS]

I appreciate that!

[@efegecili]

bro this is literally gold

[@jerrysoto5754]

Dear Sir, The equation for friction force used is only applied to calculate the maximum or limit friction. While rolling without slipping, it is usually less than Nμ. Therefore, in this case we cannot set the friction equal to Nμ

[@INTEGRALPHYSICS]

Since were solving for the limiting case, thats precisely what we can do.

[@damn7637]

Thanks teacher🙏🙏 learnt a lot

[@INTEGRALPHYSICS]

Glad to hear that

[@minhajtanim7646]

As the director of torque due to friction force is negative why there is no negative sign front of Fr.R?

[@shivmoradiya2165]

Please make a video on rolling without slipping with sphere is going uphill (because friction in it is also upwards and i dont know why?)

[@alucard5841]

this is 7 months late, but here we are:
when a ball is pushed up a hill with an initial velocity, there is no force to keep it going up, there was only an initial "kick" to give it speed, so the main force acting on the ball is gravity, which as always, it's pushing it down, and friction is always paralel tot he surface and in opposite direction to the sum of the other forces, so it points up.
but, note that friction is positive this time, since it points in the direction of the movement (speed is posite, ball is moving up, ball is getting postiive on the X axis, friction is also pointing up) and gravity is negative.

[@davewilson13]

Friction is ONLY mu x Normal if maximum. This is implied, but not stated.