1) A rectangular slab with dimensions 0.16 m x 0.24 m and mass = 1.5 kg is const

Question

1)

A rectangular slab with dimensions 0.16 m x 0.24 m and mass = 1.5 kg is constrained to rotate about an axis through its center of mass and perpendicular to the plane of the rectangle (see diagram.) A force of 2.3 N that is directed as shown in the diagram below acts on the rectangle at one corner.   

a)Determine the torque produced by the force about the axis of rotation, show steps

b) give the direction of the torque vector and if its clockwise or counter clockwise

Explanation / Answer

here moment of inertia I = (1/12)*m*(L^2 + b^2)

I = (1/12)*1.5*((0.24*0.24)+(0.16*0.16)) = 0.0104 kg m^2

torque acting on the slab = force * perepndicular
distance = F*(b/2) = 2.3*0.08 = 0.184 Nm

net torque = I*alfa

alfa = torque / I

alfa = 0.184/0.0104 = 17.69 rad/s^2 <-answer

part b)

clock wise

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