Finding Torque, Angular Velocity & Potential Energy of a Uniform Rod

In summary, the conversation discusses a uniform rod with a length of 87 m and mass of 8 kg, with a mass of 8 kg attached at one end and pivoted about the horizontal axis. The torque immediately after the system is released from the horizontal position is 10231.2 kgm^2/s^2. The angular velocity of the system as the rod passes through the vertical direction is 0.50 s^-1, calculated using the equation Στ=I*α and the conservation of energy principle. The potential energy released in going from 0 degrees to 67 degrees is still unknown.
  • #1
grouchy
73
0
A uniform rod has length 87 m and mass 8 kg. A mass of 8 kg is attached at one end. The other end of the rod is pivoted about the horizontal axis.

a) determine the torque immediately after the rod-plus-mass system is released from the horizontal position.

b) After the rod-plus-mass system is released, it rotates freely. Determine its angular velocity as the rod passes through the vertical direction. Answer in units of s^-1

c) The angle between the instantaneous position of the rod and the initial horizontal direction is 67 degrees. How much potential energy is released in going from 0 degrees to 67 degrees?
 
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  • #2
grouchy said:
A uniform rod has length 87 m and mass 8 kg. A mass of 8 kg is attached at one end. The other end of the rod is pivoted about the horizontal axis.

a) determine the torque immediately after the rod-plus-mass system is released from the horizontal position.

b) After the rod-plus-mass system is released, it rotates freely. Determine its angular velocity as the rod passes through the vertical direction. Answer in units of s^-1

c) The angle between the instantaneous position of the rod and the initial horizontal direction is 67 degrees. How much potential energy is released in going from 0 degrees to 67 degrees?

I found how to do part a

T = m(rod)gl +m(mass)gr
T = 8(9.8)(87) + 8(9.8)(43.5)
T = 10231.2 kgm^2/s^2

still got no clue how to attack b or c.
 
  • #3
grouchy said:
A uniform rod has length 87 m and mass 8 kg. A mass of 8 kg is attached at one end. The other end of the rod is pivoted about the horizontal axis.

a) determine the torque immediately after the rod-plus-mass system is released from the horizontal position.

b) After the rod-plus-mass system is released, it rotates freely. Determine its angular velocity as the rod passes through the vertical direction. Answer in units of s^-1

c) The angle between the instantaneous position of the rod and the initial horizontal direction is 67 degrees. How much potential energy is released in going from 0 degrees to 67 degrees?

Found b...
Στ=I*α

I=8*87^2/3+8*87^2
I=80736

α=0.127 rad/s^2

θ=π/2

using energy
m*g*h=.5*m*v^2=.5*I*ω^2

9.81*(8*43.5+8*87)=.5*80736*ω^2
0.50 rad/s

P.S. Any help with c?
 

FAQ: Finding Torque, Angular Velocity & Potential Energy of a Uniform Rod

1) What is torque and how is it calculated?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to the object by the perpendicular distance from the axis to the point where the force is applied.

2) How do you calculate the angular velocity of a uniform rod?

The angular velocity of a uniform rod is calculated by dividing the linear velocity at a point on the rod by the distance from the point to the axis of rotation. This can also be expressed as the change in angular displacement over a given time interval.

3) What is potential energy and how does it relate to a uniform rod?

Potential energy is the energy that an object possesses due to its position or configuration. In the case of a uniform rod, potential energy is a result of its height above a reference point. The higher the rod is positioned, the greater its potential energy.

4) Can you determine the torque, angular velocity, and potential energy of a non-uniform rod?

Yes, the calculations for torque, angular velocity, and potential energy can be applied to a non-uniform rod as well. However, the calculations may be more complex as the distribution of mass and shape of the rod may vary.

5) How does changing the mass or length of a uniform rod affect its torque, angular velocity, and potential energy?

Changing the mass of a uniform rod will directly affect its torque and potential energy, as both are dependent on the force and distance from the axis. Increasing the mass will increase the torque and potential energy. The length of the rod will also affect these values, as a longer rod will have a greater distance from the axis and therefore a higher torque and potential energy.

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