a spool of thread consists of a E. … A hollow sphere is attached to the end of a

Question

a spool of thread consists of a E. … A hollow sphere is attached to the end of a uniform rod. The sphere has a radius of 0.78 m and a mass of 0.40 kg. The rod has a length of 1.90 m and a mass of 0.56 kg. The rod is placed on a fulcrum (pivot) at X 0.48 m from the left end of the rod. (a) Calculate the moment of inertia (click for graphical table) of the contraption around the fulcrum. kg m2 (b) Calculate the torque about the fulcrum, using CCW as positive. N m (c) Calculate the angular acceleration of the contraption, using CCW as positive. rad/s2 (d) Calculate the linear acceleration of the right end of the rod, using up as positive. m/s?

Explanation / Answer

(A) moment of inertia of rod,

I1 = (0.56 x 1.90^2 / 12) + (0.56 x (1.90/2 - 0.48)^2)

I1 = 0.29217 kg m^2

of sphere:

I2 = (2 x 0.40 x 0.78^2 / 3) + (0.40 x (0.78 + 0.48)^2)

I2 = 0.79728 kg m^2

I = I1 + I2 =1.089 kg m^2

(b) torque = (0.78 + 0.48)(0.40 x 9.81 ) - ((1.90/2- 0.48) (0.56 x 9.81))

= 2.36 N m

(c) torque = I alpha

2.36 = (1.089) alpha

alpha = 2.17 rad/s^2

(d) a = alpha r

a = 2.17 x (1.90 - 0.48) = 3.08 m/s^2

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