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Two thin circular discs of mass 2 Kg and radius 10 cm each are joined by a rigid massless rod of length 20 cm. The axis of the rod is along the perpendicular to the planes of the disk through their centres. This object is kept on a truck in such a way that the axis of the object is horizontal and perpendicular to the direction of motion of the truck. Its friction with the floor of the truck is large enough so that the object can roll on the truck without slipping. Take x-axis as the direction of motion of the truck and z-axis as the vertically upwards direction. If the truck has an acceleration 9 m/s 2 , calculate: (i) the force of friction on each disk. (ii) the magnitude and direction of the frictional torque acting on each disk about the centre of mass O of the object. Express the torque in the vector form in terms of unit vectors i, j and k in x, y and z directions.

Two thin circular discs of mass 2 Kg and radius 10 cm each are joined by a rigid massless rod of length 20 cm. The axis of the rod is along the perpendicular to the planes of the disk through their centres. This object is kept on a truck in such a way that the axis of the object is horizontal and perpendicular to the direction of motion of the truck. Its friction with the floor of the truck is large enough so that the object can roll on the truck without slipping. Take x-axis as the direction of motion of the truck and z-axis as the vertically upwards direction. If the truck has an acceleration 9 m/s2, calculate:

circular discs

(i) the force of friction on each disk.
(ii) the magnitude and direction of the frictional torque acting on each disk about the centre of mass O of the object. Express the torque in the vector form in terms of unit vectors i, j  and k  in x, y and z directions.


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1 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

Dear Jay,

Let I be the moment of inertia of each disk. let radius=r and angulat acceleration=alpha and friction on each disk=f,mass of each disk=m =2kg

i)2*9m/s2-2*f=2r*alpha

2rf=I*alpha,solve for the two unknowns f and alpha

ii)let centre of mass be origin.

frictional torque on disk1 about origin=(-10j-10k)×(-fi)

frictional torque on disk2 about origin=(+10j-10k)×(-fi)

 

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