Finding the angular speed of a hinged rod without using torque or acceleration.

In summary, the conversation discusses the calculation of the angular acceleration of a rod that is falling from a starting position of 30 degrees above horizontal. The centre of mass of the rod is at the middle and the force responsible for torque acts downwards. The moment of inertia of the rod about the end is calculated using the parallel axis theorem and the resulting angular acceleration is found to be 3g/4l. However, this approach does not take into account the changing angle of the rod as it falls. The conversation suggests finding an alternative approach that does not involve torques and accelerations.
  • #1
Crystal037
167
7
Homework Statement
A rod of length 50cm is pivoted at one end. It is raised such that it makes an angle 30 degrees from the horizontal as shown and released from rest. It's angular speed when it passes through the horizontal will be
Relevant Equations
wf^2 - wi^2 = 2*alpha*theta,
w=angular velocity
Torque =F*r
Torque =I*alpha
The centre of mass of the rod would be at the middle of the rod i.e. at
l/2=[50*10^(-2)]/2
The force responsible for torque will be acting downwards = mg
The Torque = mg*l/2*sin(30) =mg*l/4
We know that Torque=I*alpha
Hence alpha = mg*l/(4*I)
Moment of inertia of rod about the end= ml^2/12 + ml^2/4 (parallel axis theorem) =ml^2/3
Hence alpha=3mgl/(4ml^2) =3g/4l
Now wf^2- wi^2 =2*alpha *theta
=2*3g/4l*pi/6 since theta =pi/6 since it starts from rest wi=0
Hence wf^2 = 2*3*10/(4*0.5)*pi/6
Hence wf= 3.96
But the answer is sqrt(30). Apparently they haven't considered the angle pi/6. Where am I wrong?
 
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  • #2
Crystal037 said:
The Torque = mg*l/2*sin(30) =mg*l/4
Two problems with that.
The initial position is 30 degrees above horizontal, not 30 degrees from vertical.
The angle will change as the rod falls, so the angular acceleration increases.

Can you think of an approach that avoids torques and accelerations?
 

1. What is a hinged rod?

A hinged rod is a type of mechanical component that consists of a straight rod attached to a hinge or pivot point at one end. This allows the rod to rotate freely around the hinge, while the other end remains fixed.

2. What is angular speed?

Angular speed, also known as rotational speed, is a measure of how fast an object is rotating around a fixed point. It is typically measured in radians per second (rad/s) or revolutions per minute (rpm).

3. How is angular speed related to hinged rods?

Hinged rods are often used in rotational motion systems, where the angular speed of the rod determines the speed and direction of the rotation. This is because the rotation of the rod around the hinge is directly related to its angular speed.

4. What factors affect the angular speed of a hinged rod?

The angular speed of a hinged rod can be affected by various factors, including the length of the rod, the distance of the hinge from the fixed end, and the amount of force or torque being applied to the rod.

5. How is angular speed calculated for a hinged rod?

The angular speed of a hinged rod can be calculated using the formula ω = v/r, where ω is the angular speed in radians per second, v is the linear speed of the rod, and r is the distance from the hinge to the fixed end of the rod. Alternatively, it can also be calculated using ω = 2πf, where f is the frequency of rotation in hertz (Hz).

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