Problem 1: you have a horizontal grindstone (a disk) that is 85 kg, has a 0.35 m radius, is turning at 89 rpm (in the positive direction), and you press a steel axe against the edge with a force of 22 n in the radial direction.

part (a) assuming that the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstone in rad/s2.
numeric : a numeric value is expected and not an expression.
α =

part (b) what is the number of turns, n, that the stone will make before coming to rest?
numeric : a numeric value is expected and not an expression.
n =

problem 2: a pulley consists of a large disk of radius r and a small disk of radius r that are welded together and mounted on a horizontal frictionless axle through their common centers. the moment of inertia of this pulley is i. a box containing a turkey of mass m is suspended from a rope wound around the large disk; a box containing a pumpkin of mass m is suspended from a rope wound around the small disk. the ropes do not slip on the disks. the system is released from rest and the turkey begins to descend, while the pumpkin is being lifted up.

derive an expression for the magnitude of the angular acceleration a of the pulley, in terms of system parameters. assume that a counterclockwise motion of the pulley is the positive direction.
schematicchoice :

problem 3: a solid sphere of mass m and radius r rolls without slipping down a rough incline that makes an angle θ with the horizontal.

find the magnitude of the linear acceleration a of the sphere.
schematicchoice :