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brilliants [131]
3 years ago
7

A pendulum is constructed from a heavy metal rod and a metal disk, both of uniform mass density. The center of the disk is bolte

d to one end of the rod, and the pendulum hangs from the other end of the rod. The rod has a mass of =1.0 kg and a length of =49.8 cm. The disk has a mass of =4.0 kg and a radius of =24.9 cm. The acceleration due to gravity is =9.8 m/s2.
The pendulum is held with the rod horizontal and then released. What is the magnitude of its angular acceleration at the moment of release?
Physics
1 answer:
Setler79 [48]3 years ago
5 0

Answer: α = 20.4 rad/s²

Explanation:

α = τ/I

If we model it as a rod and a point mass, the moment of inertia

I = mL²/3 + ML² = 0.498²)(1.0/3 + 4.0) = 1.07 kg•m²

torque will be

τ = 1.0(9.8)(0.498/2) + 4.0(9.8)(0.498) = 21.96 N•m

α = 21.96 / 1.07 = 20.43...

Another possibility is that we model the large mass as a disc and apply the parallel axis theorem

I = mL²/3 + ½MR² + ML²

I =  1.07 + ½(4.0)0.249² = 1.19 kg•m/s

then

α = 18.45... 18.5 rad/s²

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