A square plate with sides 1.9 m in length can rotate around an axle passing thro

Question

A square plate with sides 1.9 m in length can rotate around an axle passing through its center of mass (CM) and perpendicular to its surface (see figure below). There are four forces acting on the plate at different points. The rotational inertia of the plate is

23 kg · m2.

Use the values given in the figure to answer the following questions. (Assume = 40°. Express your answers in vector form.)

(a) What is the net torque acting on the plate?

N · m

(b) What is the angular acceleration of the plate?

rad/s2

Explanation / Answer

the distance from CM to vertices are sqrt(2)*(1.9/2) = 1.34 m

torque due to 30 N is -(1.34*30)*sin(45) = -28.42 N-m

Torque due to 60 N is (-1.34*60*sin(45)) = -56.85 N-m

Torque due to 40 N is (1.34*40*sin(85)) = 53.4 N-m

Torque due to 20 N is (-1.34*20*sin(45)) = -18.95 N-m

Net torque is (-28.42-56.85+53.4-18.95) = -50.82 N-m

Net torque is 50.82 N-m in clockwise direction

But torque T = I*alpha

angular accelaration is alpha = T/I = 50.82/23 = 2.209 rad/s^2 in clockwise direction

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