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1. In the figure below, a zero-mass bar is connected to a sphere on one end and

ID: 1785003 • Letter: 1

Question

1. In the figure below, a zero-mass bar is connected to a sphere on one end and a smooth pin on the other. Show all your work and equations clearly, do not skip steps. Find body moment of inertia about z-axis through point O (at the pin). 5 points a. b. Find angular acceleration of the body. Sphere: Mass M Radius R Pin 5 points Find the acceleration of the center of mass, when the system is released from rest using relative acceleration equation. 5 points Prove (with equations) that the force exerted on the pin (in y-direction) equals to the formula below. Show each step clearly using a FBD, c. d. do not just arbitrarily make the math work out. 5 points

Explanation / Answer

a)The moment of inertia can be determined using parallel axis theorem

Moment of inertia of sphere about an axis passing through its center and parallel to z axis = (2/5)MR2

Moment of inertia of sphere about axis through pin =I= (2/5)MR2 + ML2

b)Torque acting about pin =T= MgL

Angular acceleration = T/I =MgL / [(2/5)MR2 + ML2] = gL/[(2/5)R2+L2]

c)Acceleration of center of mass = gL2/[(2/5)R2+L2]