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A cotton reel of mass m and moment of in...

A cotton reel of mass `m` and moment of inertia `I` is kept at rest on as smooth horizontal surface. The reel has inner and other radius `r` and `R` respectively. A horizontal force `F` starts actings as shown in figure. Find the

a. acceleration of the centre of mass of reel.
b. angular acceleration of the reel
c. net acceleration of point of contact.

Text Solution

Verified by Experts

a. From force equation `F=maimpliesa=F.m`……..i

b. We can apply torque equatioinn about centre of mass. From torque equation
`Fr=Ialphaimplies alpha=(Fr)/I`……….ii
c. Acceleration of `'P':veca_(P)=veca_(P,O)+veca_(O)`
`implies a_(P)=(-alphaR)+a=a-alphaR=(a-(Fr)/I)R`
Hence acceleration of point of contact will be `a-((Fr)/I)R` in forward direction.
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