The disk rotates about a fixed axis through point O with a clockwise angular velocity ω0 = 16 rad/s and a counterclockwise angular acceleration α0 = 5.6 rad/s2 at the instant under consideration. The value of r is 280 mm. Pin A is fixed to the disk but slides freely within the slotted member BC. Determine the velocity and acceleration of A relative to slotted member BC and the angular velocity and angular acceleration of BC. The relative velocity and acceleration are positive if they point from B to C and negative if they point from C to B. The angluar velocity and angular accelerations are positive if counterclockwise, negative if clockwise.

V = 4.48m/s a = 1.57m/s²

Explanation:

ω₀ = 16rad/s

α₀ = 5.6rad/s²

r = 280mm = 0.28m

a = ?

v = ?

Angular velocity (ω₀) = velocity of acceleration / length of path

ω₀ = v / r

V = ω₀ * r

V = 16 * 0.28

V = 4.48m/s

Acceleration = ?

Angular acceleration α₀ = angular velocity (ω) / time take (t)

α₀ = ω / t equation i

But acceleration (a) = velocity (v) / time (t)

a = v / t

t = v / a

Put t = v / a into equation i

α₀ = ω / (v / a)

α₀ = ω * a / v

α * v = ω * a

a = (α * v) / ω

a = (5.6 * 4.48) / 16

a = 1.568m/s²

a = 1.57m/s²

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day