Question

During a hard drive crash the read/write head scrapes against the disk with a coefficient of kinetic friction of µk and normal force of N. Assume that just before the head crash the disk is rotating at ω0 rad/s, and the distance of the head from the disk axis is r. You can ignore any friction at the bearing (rotational axis of the disk). Assume that the disk is uniform, and has radius R and mass M. What is the angular acceleration associated with the torque from the crashed disk head?

Answer 1

Answer:

 α = $\frac{2 \mu \ N}{m \ r}$

Explanation:

For this exercise we use Newton's equation for rotational motion

           ∑ τ = I α

the troque is

           α = Fr .r

the moment of inertia of a cylinder is

           I = ½ m r²

we substitute

         fr r = (½ m r²) α

the expression friction is

         fr = μ N

we substitute

         μ N r = ½ m r² α

       

         α = $\frac{2 \mu \ N}{m \ r}$