The 30-kg disk is originally spinning at v = 125 rad>s. If it is placed on the ground, for which the coefficient of kinetic friction is μC = 0.5, determine the time required for the motion to stop. What are the horizontal and vertical components of force which the member AB exerts on the pin at A during this time? Neglect the mass of AB.

t = 3.82 s

Ax = 147 N (←)

Ay = 294 N (+↑)

Explanation:

Given

m = 30.0 Kg

ωinitial = 125 rad/s

ωfinal = 0 rad/s

μC = 0.5

R = 0.3 m

t = ?

Ax = ?

Ay = ?

For the disk, we can apply

∑ τ = I*α

where I = m*R²/2

then

⇒ R*Ffriction = (m*R²/2) * α

⇒ R * (-μC*N) = R * (-μC*m*g) = (m*R²/2) * α

⇒ α = - 2*μC*g / R

⇒ α = - 2 * (0.5) * (9.8) / 0.3 = - 32.666 rad/s²

we can use the equation to get t:

α = Δω / t ⇒ t = Δω / α = (0 - 125) / (-32.666)

⇒ t = 3.82 s

The horizontal and vertical components of force which the member AB exerts on the pin at A during this time are

∑ Fx = 0 (+→)

Ax - Ffriction = 0

⇒ Ax = Ffriction = μC*m*g = (0.5) * (30) * (9.8) = 147 N

⇒ Ax = 147 N (←)

∑ Fy = 0 (+↑)

⇒ Ay - m*g = 0

⇒ Ay = m*g

⇒ Ay = 30*9.8 = 294 N

⇒ Ay = 294 N (+↑)