Kinetics of Rigid Bodies: Torque and Acceleration Calculation

In summary, The problem involves calculating the torque needed to accelerate an electric motor rotor of mass 200 kg and a radius of gyration of 150 mm from rest to 1,500 rev/min in 6 seconds. The equation ƩMO = Iα is used, where I is equal to 1/2 (mr2) and the angular acceleration α can be found using the kinematic equations of rotational motion. The radius of gyration formula is r = \sqrt{I/m}. Overall, this involves using the correct equations and understanding how they are related to solve the problem.
  • #1
Rob K
33
0

Homework Statement


The rotor of an electric motor of mass 200 kg has a radius of gyration of 150 mm. Calculate the torque required
to accelerate it from rest to 1,500 rev/min in 6 seconds. Friction resistance may be neglected.

Homework Equations


ƩMO = Iα
I = 1/2 (mr2
I am really really stuck here, I don't know what equations I need to use, if this were a straight line question I would use v = u + at, but it isn't so that is wrong


The Attempt at a Solution


All I have so far is this
I = 1/2 (mr2
I = 0.5 * 200 * 0.152
I = 2.25 kgm2

Really lost. I just need some pointers please.

Kind regards

Rob
 
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  • #2
In calculating I, the radius of gyration is not the radius of a disk. You can look up the formula for it, which is [itex]r = \sqrt{I/m} [/itex] (and note how it is derived).

You can find the angular acceleration α using the kinematic equations of rotational motion (watch units).
 
  • #3
Brilliant, those are the words I didn't know to find the equation I couldn't find of variables I couldn't relate.

Found them all.

Thank you
 

1. What is the difference between translational and rotational motion of rigid bodies?

Translational motion refers to the linear movement of a rigid body, where all points on the body move in the same direction and at the same speed. Rotational motion, on the other hand, refers to the movement of a rigid body around a fixed axis, where different points on the body move at different speeds and in different directions.

2. How do you calculate the acceleration of a rigid body?

The acceleration of a rigid body can be calculated using Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In rotational motion, the moment of inertia is also taken into account.

3. What is the principle of conservation of angular momentum?

The principle of conservation of angular momentum states that the total angular momentum of a system remains constant unless acted upon by an external torque. This means that in the absence of external forces, the angular momentum of a rigid body will remain constant.

4. How does the distribution of mass affect the rotational motion of a rigid body?

The distribution of mass affects the rotational motion of a rigid body through its moment of inertia. The further the mass is from the axis of rotation, the larger the moment of inertia and the more difficult it is to change the body's rotational motion.

5. Can a rigid body have both translational and rotational motion at the same time?

Yes, a rigid body can have both translational and rotational motion at the same time. This is known as rolling motion, where the body is simultaneously moving in a straight line and rotating around an axis. An example of this is a rolling wheel.

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