Two blocks are placed at the ends of a horizontal massless board, shown below. T

Question

Two blocks are placed at the ends of a horizontal massless board, shown below. The board is kept from rotating and rests on a support that serves as an axis of rotation. Find the moment of inertia of this system relative to the axis. Determine the magnitude of the angular acceleration when the system released and is allowed to rotate. A car moves at a constant speed along a straight line as it approaches a circular turn. In which of the following motions is the car in equilibrium (sum of forces and torques equals zero)? (check all that apply) As it moves along the straight line toward the circular turn As it is going around the turn As it moves away from the turn along a straight line

Explanation / Answer

1)

Given m1 = 12 kg

m2 = 4 kg

r1 = 0.6 m

r2 = 1.4 m

a)

moment of inertia of the syatem is

I = m1 * r1^2 + m2 * r2^2

I = (12 * 0.6^2) + (4 * 1.4^2)

I = 12.16 kg-m^2

b)

torque T = I * alpha

m1*g *r1 - (m2 *g *r2) = I * alpha

(12 * 9.8 * 0.6) - (4*9.8*1.4) = 12.16 * alpha

alpha = 1.29 rad/s^2

2)

the car is in equillibrium

a) as it moves along a straight line

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