3. A heavy, circular merry-go-round has a radius of 1.75 m and a moment of inert

Question

3. A heavy, circular merry-go-round has a radius of 1.75 m and a moment of inertia (about its central axis) of 450. kg m. (7 pts.) Four children, standing on the ground, all pull simultaneously with four different forces on the edge of the merry-go-round: child A: 530. N, clockwise (CW), tangential child B: 350N, counter-clockwise (CCW), tangential child C: 200. N, exactly away from center child D: 380. N, counter-clockwise (CCW), at an angle 120. away from the center TOP VIEW: Find the resulting angular acceleration of the merry-go- round at the moment described. Will it be CCW or CW? (Assume that the merry-go-round's axle is frictionless.) Show your work completely F120

Explanation / Answer

Given,

R = 1.75 m ; I = 450 kg-m^2

Fa = 530 N ; Fb = 350 N ; Fc = 200 N ; Fd = 380 N

Let CW be negative

we know that torque is:

Tau = F r sin(theta)

Tau-a = -530 x 1.75 x sin90 = -927.5 N-m

Tau-b = +350 c 1.75 x sin90 = 612.5 N-m

tau-c = 200 x 1.75 x sin0 = 0 N-m

tau-d = 380 x 1.75 x sin(-120) = -575.91 N-m

Net Torque = -927.5 + 612.5 -575.91 = -890.91 N-m

also, toruq = I alpha

alpha = Net torue/I

alpha = -890.91/450 = -1.98 rad/s^2

Hence, alpha = 1.98 rad/s^2 ; Clockwise direction

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