Help with a torque-rotational-inertia-force question please

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In summary, a cylindrical fishing reel with a moment of inertia of 6.22×10-4 kg·m2 and a radius of 4.44 cm has a friction clutch that exerts a restraining torque of 1.34 N·m when a fish pulls on the line. When the reel begins to spin with an angular acceleration of 66.5 rad/s2 due to the fish pulling on the line, the force of the fish on the line can be calculated using the equation T = Iα, where T is the total torque, I is the moment of inertia, and α is the angular acceleration. By subtracting the resisting torque of the reel from the total torque, we can determine the additional torque supplied by
  • #1
Windwaker2004
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A cylindrical fishing reel has a moment of inertia of I=6.22×10-4 kg·m2 and a radius of 4.44 cm. A friction clutch in the reel exerts a restraining torque of 1.34 N·m if a fish pulls on the line. The fisherman gets a bite, and the reel begins to spin with an angular acceleration of 66.5 rad/s2. What is the force of the fish on the line?

I would like to know if the proper acceleration to use here to calculate force would be the tangential acceleration. Also, when I use T = Fxr... does the value of F get subtracted from the force the fish is pulling with? I also can't figure out how to use the inertia in this because if I solve for mass using I = MR^2 ... that's the mass of the reel which makes no sense in using to calculate force. Anyway any help would be greatly appreciated! Thanks in advance!
 
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  • #2
You just work with angular acceleration.

The eqn to use here is T= Iα

You are given the values of I and α, so what is the torque providing this (angular) accln ?

You are given the resisting torque of the reel, so what must be the additional torque supplied by the fish ?

And finally, what must be the force giving this torque ?
 
  • #3
Thank you so much for your help. I made it a lot more complicated than that method. I worked it out and got the correct answer. Thanks again!
 

1. What is torque and how is it related to rotational inertia and force?

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 an object by the distance from the axis of rotation. Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to rotational motion. Torque is directly related to rotational inertia, as a larger moment of inertia requires more torque to produce the same amount of rotational acceleration. Force, on the other hand, is the push or pull that causes an object to move or change its motion. In rotational motion, force is responsible for creating torque.

2. How do I calculate torque in a rotational system?

To calculate torque, you will need to know the force applied to an object and the distance from the axis of rotation at which the force is applied. Torque is then calculated by multiplying the force by the distance (T= F x d). The unit for torque is Newton-meters (Nm) in the SI system and foot-pounds (ft-lbs) in the Imperial system.

3. What is the relationship between torque and angular acceleration?

The relationship between torque and angular acceleration is described by Newton's Second Law of Motion for rotational systems, which states that the torque applied to an object is equal to the moment of inertia multiplied by the angular acceleration (T= I x α). This means that a larger torque will result in a larger angular acceleration, and vice versa.

4. How does rotational inertia affect the stability of an object?

Rotational inertia plays a crucial role in determining the stability of an object in rotational motion. The greater the moment of inertia of an object, the more resistant it is to changes in its rotational motion. This means that objects with a larger rotational inertia will be more stable and less likely to tip over.

5. Can you provide an example of a real-life application of torque and rotational inertia?

A common real-life example of torque and rotational inertia is the motion of a bicycle wheel. When a force is applied to the pedals, it creates torque on the wheel, causing it to rotate. The moment of inertia of the wheel helps to maintain the stability of the bicycle, making it easier to balance and steer. Moreover, the rotational inertia of the wheels also helps to store and release energy, making it easier to pedal and maintain a constant speed.

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