Dynamics of Rotational Motion and hinge

[denny2]

One end of a thin, uniform rod is connected to a frictionless hinge as shown in Figure 1. The rod has a length of 0.8 mand a mass of 2 kg. It is held up in the horizontal position (θ=90∘) and then released.
1)Calculate the angular velocity of the rod at θ=90∘.
2)Calculate the angular acceleration of the rod at θ=90∘.
3)Calculate the angular velocity of the rod at θ=60∘
4)Calculate the angular acceleration of the rod at θ=60∘
5)Calculate the angular velocity of the rod at θ=0∘.
6)Calculate the angular acceleration of the rod at θ=0∘.

Homework Equations

mgh=1/2 Iw^2
a = ((mgcos)1/2)/I

The Attempt at a Solution

I got these answers and only 1 and 6 were correct
1)0 rad/s
2)74 rad/s^2
3)8.6 rad/s
4)64 rad/s^2
5)12 rad/s
6)0 rad/s^2

Any help is appreciated thank you :)

 

[drvrm]

Calculate the angular acceleration of the rod at θ=90∘.
3)Calculate the angular velocity of the rod at θ=60∘
4)Calculate the angular acceleration of the rod at θ=60∘
5)Calculate the angular velocity of the rod at θ=0∘.

you are having problem with above - so check expression for angular acceleration.
moment of inertia xangular acceleration = torque on the rod =forcex the the perpendicular distance from the axis of rotation
and for angular velocity one can use the work- energy conversion
work done by a torque is torquex angular displacement= rotational energy

 

[haruspex]

One end of a thin, uniform rod is connected to a frictionless hinge as shown in Figure 1. The rod has a length of 0.8 mand a mass of 2 kg. It is held up in the horizontal position (θ=90∘) and then released.
1)Calculate the angular velocity of the rod at θ=90∘.
2)Calculate the angular acceleration of the rod at θ=90∘.
3)Calculate the angular velocity of the rod at θ=60∘
4)Calculate the angular acceleration of the rod at θ=60∘
5)Calculate the angular velocity of the rod at θ=0∘.
6)Calculate the angular acceleration of the rod at θ=0∘.

Homework Equations

mgh=1/2 Iw^2
a = ((mgcos)1/2)/I

The Attempt at a Solution

I got these answers and only 1 and 6 were correct
1)0 rad/s
2)74 rad/s^2
3)8.6 rad/s
4)64 rad/s^2
5)12 rad/s
6)0 rad/s^2

Any help is appreciated thank you :)

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