A physical pendulum is constructed of a 34 cm long piece of wooden dowel with a

Question

A physical pendulum is constructed of a 34 cm long piece of wooden dowel with a mass of 525 grams and a radius of 0.9 cm. Attached at one end of the pipe is a hoop with a radius of 4 cm and a mass of 1.8 kg as shown. The pendulum is released from the 12:00 position and allowed to rotate about the other end.

a. What is the maximum angular speed of any part of the pendulum?  rad/s
b. What is the maximum speed of any part of the pendulum?  m/s

A physical pendulum is constructed of a 34 cm long piece of wooden dowel with a mass of 525 grams and a radius of 0.9 cm. Attached at one end of the pipe is a hoop with a radius of 4 cm and a mass of 1.8 kg as shown. The pendulum is released from the 12:00 position and allowed to rotate about the other end. a. What is the maximum angular speed of any part of the pendulum? rad/s b. What is the maximum speed of any part of the pendulum? m/s

Explanation / Answer

location of center of mass from axis h = ((34*525)+(1800*38))/(525+1800) = 37.1 cm

moment of inertia of dowel I1 = (1/3)*m*L^2 = (1/3)*0.525*0.34^2 = 0.02 kg m^2

moment of inertia of ring I2 = M*R^2 + M*L^2 = (1.8*0.04^2) + (1.8*0.34^2) = 0.211 kgm^2

from energy conservation

change in PE = change in KE

(M+m)*g*2*h = (1/2)*I*w^2

2*(1.8+0.525)*9.8*0.371 = (1/2)*(0.02+0.211)*w^2

w = 12.1 rad/s    <<<<<--------answer

part(b)

vmax = w*(L+d)

d = diameter

Vmax = 12.1*(0.34+0.08) = 5.1 m/s <<<<----------answer

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