Rigid Body Kinetics: Angular Acceleration of Rod w/ Friction Torque

In summary, a long slender rod with a mass of 0.66 kg and a length of 648.0 mm has a friction torque of 0.41 Nm at the hinge. The angular acceleration of the rod when it is 38 degrees below the horizontal can be found using the equation torque = moment of inertia x angular acceleration, where the moment of inertia for a rod is (1/12)*m*(l^2). However, the moment of inertia must be calculated about a specific axis and the torque due to friction must also be included in the calculation of net torque.
  • #1
gus_lyon
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Homework Statement


A long slender rod has a mass of 0.66 kg and a length of 648.0 mm. The friction torque at the hinge is 0.41 Nm.

What is the angular acceleration of the rod when it is 38 degrees below the horizontal?


Homework Equations





The Attempt at a Solution



Torque = moment of inertia x angular acceleration
Moment of inertia for a rod = (1/12)*m*(l^2)
= (1/12)*0.66*(0.648^2) = 0.0231 Kgm^2
Torque = Radius * Force
= (0.648*cos(38))*(9.81*0.66) = 3.306 Nm

Angular acceleration = Torque/Moment of inertia
= 3.306/0.0231 = 143.12

Which is wrong.
 

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  • #2
gus_lyon said:
Moment of inertia for a rod = (1/12)*m*(l^2)
That's the moment of inertia about what axis?

And when you find the net torque, be sure to include the torque due to friction.
 

1. What is the definition of angular acceleration in rigid body kinetics?

Angular acceleration in rigid body kinetics refers to the rate of change of angular velocity over time. It is measured in radians per second squared (rad/s^2) and is a vector quantity, indicating both the magnitude and direction of the angular change.

2. How is friction torque calculated in a rotating rod?

Friction torque in a rotating rod is typically calculated using the formula T = μR, where μ is the coefficient of friction and R is the distance between the axis of rotation and the point where the force of friction is acting. This formula assumes that the force of friction is acting tangentially to the surface of the rod and in the opposite direction of the motion.

3. What factors affect the angular acceleration of a rod with friction torque?

The angular acceleration of a rod with friction torque can be affected by several factors, including the coefficient of friction, the distance from the axis of rotation to the point where the force of friction is acting, and the mass and shape of the rod. Additionally, the angular acceleration can also be influenced by external forces acting on the rod, such as gravity or applied torque.

4. How does the presence of friction torque affect the overall motion of a rotating rod?

Friction torque can cause a decrease in the angular velocity of a rotating rod, leading to a decrease in the overall motion of the rod. This is because the force of friction acts in the opposite direction of the motion, creating a resistance that must be overcome. The magnitude of the friction torque will determine the extent to which the motion is affected.

5. Can the angular acceleration of a rod with friction torque ever be zero?

Yes, the angular acceleration of a rod with friction torque can be zero if the sum of all torques acting on the rod is also zero. This can occur when the force of friction is equal and opposite to the applied torque, resulting in a net torque of zero and no change in angular velocity. However, in most cases, there will be some degree of angular acceleration due to other external forces acting on the rod.

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