Find: 1) Calculate the angular velocity of the rod at ? =90?. 2) Calculate the a

Question

Find:

1) Calculate the angular velocity of the rod at ?=90?.

2) Calculate the angular acceleration of the rod at ?=90?.

3)Calculate the angular velocity of the rod at ?=60?.

4)Calculate the angular acceleration of the rod at ?=60?

5)Calculate the angular velocity of the rod at ?=0?.

6)Calculate the angular acceleration of the rod at ?=0?.

Thanks!

One end of a thin, uniform rod is connected to a frictionless hinge as shown in (Figure 1). The rod has a length of 0.7 m and a mass of 2 kg. It is held up in the horizontal position ( 90°) and then released. Figure 1 ,1 of 1 of 1

Explanation / Answer

1)

angular velocity w = 0
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(2)

net torque = I*alfa

m*g*L/2 = (1/3)*m*L^2*alfa

2*9.8*0.7/2 = (1/3)*2*0.7^2*alfa

alfa = 21 rad/s^2

============

(3)

potential energy at theta = 60 = U2 = m*g*L/2*(1-cos60)

KE at 60 K2 = 0.5*I*w1^2

2*9.8*0.7/2 = (0.5*(1/3)*2*0.7^2*w1^2) + (2*9.8*0.7/2*(1-cos60))

w1 = 4.58 rad/s

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(4)

net torque = I*alfa

m*g*L/2*sin60 = (1/3)*m*L^2*alfa

2*9.8*0.7/2*sin60 = (1/3)*2*0.7^2*alfa

alfa = 18.18 rad/s^2

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5)

initial potential energy U1 = m*g*L/2

at the lowest point K2 = 0.5*I*w^2

U2 = 0

I = moment of inertia = (1/3)*M*L^2

from energy conservation

K2 = U2

(0.5*(1/3)*2*0.7^2*w^2) = 2*9.8*0.7/2

w = 6.48 rad/s

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