1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# A uniform disc of mass m and radius R rolls without slipping up a rough inclined plane at an angle of 30o with the horizontal. If the coefficient of static and kinetic friction are each equal to μ and the forces acting on the disc are gravity and contact force, then find the direction and magnitude of the friction force acting on it.

Open in App
Solution

## Since disc does not slip, friction is static and static friction can have any value between 0 and μN: Component of mg parallel to the plane is mgsinθ which is opposite to the direction of motion of the centre of mass decreases. For pure rolling the relation vc.m=ωR must be obeyed. Therefore ω must decreases. Only friction can provide a torque about the centre.Toque sue to friction must 0be opposite to the →ω. Therefore, friction force will act up the plane.Now, for translation motionmg sinθ−f=m acm (i)For rotational motionfR=Iα, where I=M.I. of the disc about centre.I=acmR as acm=αR⇒acm=fR2I (ii)From (i) and (ii) we get,f=mgsinθ1+mR2IPutting the value of θ and I, we getf=mg/6

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Rubbing It In: The Basics of Friction
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program