You have a horizontal grindstone (a disk) that is 85 kg, has a 0.31 m radius, is turning at 88 rpm (in the positive direction), and you press a steel axe against the edge with a force of 21 N in the radial direction.

a) assuming the kinetic coefficient of friction between steel and stone is. 2, calculate the angular acceleration of the grindstone in rad/s^2

b) how many turns will the stone make before coming to rest

moment of inertia of wheel

I = 1/2 mr², m is mass and r is radius of disk.

=.5 x 85 x. 31²

= 4.08425 kg m²

88rpm

= 1.467 x 2π rad / s

= 9.21 rad / s

force of friction acting = 21 x. 2

= 4.2 N

torque produced by friction to stop it

= friction x radius

= 4.2 x. 31

= 1.302 Nm

angular deceleration = Torque / moment of inertia

= 1.302 / 4.08425

=.31878 rad / s²

angular deceleration = -.31878 rad / s²

b)

initial angular speed ω₁ = 9.21

Final angular speed ω₂ = 0

angle of turn = θ radian

ω₂² = ω₁ ² - 2 αθ, α is angular deceleration

0 = 9.21² - 2 x. 31878 θ

θ = 133.04 radian

no of turns = 133.04 / 2π

= 21.18 turns.