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

To calculate the angular acceleration associated with the torque from the crashed disk head, you need to determine the torque and the moment of inertia of the disk, which can be found using relevant formulas.

Step-by-step explanation:

In this scenario, the angular acceleration associated with the torque from the crashed disk head can be calculated using the formula:

Angular acceleration (α) = Torque (τ) / Moment of Inertia (I)

To find the torque, we need to calculate the force of friction exerted by the head and the distance of the head from the disk axis. The force of friction can be found using the formula:

Force of friction (F) = coefficient of kinetic friction (µk) * normal force (N)

Once we have the torque and the moment of inertia of the disk, we can calculate the angular acceleration.

Answer 2

α =
`(2 \mu \ N)/(m \ r)`

Step-by-step 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 =
`(2 \mu \ N)/(m \ r)`