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A uniform disc of mass m, radius R is pl...

A uniform disc of mass `m`, radius `R` is placed on a smooth horizontal surface. If we apply a horizontal force `F` at `P` as shown in the figure. If `F = 4 N, m= .1 kg, R = 1 m` and `r = 1/2 m` then, find the:

angular acceleration of the disc. `(rads^(-1))`

Text Solution

Verified by Experts

The correct Answer is:
5
From the geometry of the arranement we observe that the ends `A` and `B` side on the horizontal and vertical surfaces with velocities `v_(A)` and `v_(B)` respectively, where `v_(A)=v` (given) and `v_(B)` is assumed. As per the procedure, let us drop perpediculars `AX` and `BY` from `A` and `B` respectively onto their lines of motion (`vecv_(A)` and `vecv_(B)`). We observe that the perpendicular intersect at `P`. Then `P` is the instantaneous axis of rotation.

Since `v_(P)=0`
we have `omega_(BP)=omega_(AP)(=omega)`
substituting `PA=lcostheta` and `v_(A)=v`
We have `omega=v/(costheta)=4/(1.4/5)=5rads^(-1)`
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