Combined rotational and translational motion

In summary, the total kinetic energy of a long thin rod relative to a laboratory frame rotating around an axis with angular velocity w and translational velocity Vaxis can be calculated using the formula: Total KE = 1/2 M (Vaxis sq) + 1/2 I (w sq), where M is the mass of the rod, L is the length of the rod, and I is the moment of inertia (1/3 M (L sq)). The endpoint velocity of the rod can affect the maximum kinetic energy, with a maximum velocity of one mach when L*w is equal to Vaxis.
  • #1
e2m2a
354
11

Homework Statement



I need to determine the total kinetic energy of a long thin rod relative to a laboratory frame which rotates around an axis at an angular velocity w and the axis moves at a constant translational velocity. The mass of the rod is M and the length of the rod is L. The translational velocity of the axis is Vaxis.

Homework Equations


Moment of Inertia, I, of rod is: 1/3 M (L sq) (This is because the rod rotates at one end).


The Attempt at a Solution


I believe the total kinetic energy should be: Total KE = 1/2 M (Vaxis sq) + 1/2 I (w sq).
Is this correct?
 
Physics news on Phys.org
  • #2
e2m2a said:
[Moment of Inertia, I, of rod is: 1/3 M (L sq) (This is because the rod rotates at one end).


The Attempt at a Solution


I believe the total kinetic energy should be: Total KE = 1/2 M (Vaxis sq) + 1/2 I (w sq).
Is this correct?
Hello e2m2a
The moment of inertia is correct and addition of energies too. Is there some relation of the tangential and the rotational velocities. Remind that the endpoint velocitie for a whip is one mach. The maximum is there when the endpoint of the rods velocity L*w adds up to Vaxis.
greetings Janm
 

1. What is combined rotational and translational motion?

Combined rotational and translational motion is when an object is simultaneously moving both in a straight line (translation) and rotating around a fixed axis (rotation).

2. What is the difference between rotational and translational motion?

Rotational motion is when an object moves around a fixed point or axis, while translational motion is when an object moves from one location to another in a straight line.

3. How is combined rotational and translational motion calculated?

The combined motion is calculated by combining the equations for rotational motion (using angular velocity and acceleration) and translational motion (using linear velocity and acceleration).

4. What is the relationship between rotational and translational motion?

In combined motion, the two types of motion are interdependent and affect each other. For example, an object's rotational motion can affect its linear velocity and vice versa.

5. What are some real-life examples of combined rotational and translational motion?

A spinning top, a car driving around a curve, and a planet orbiting around a star are all examples of combined rotational and translational motion. Other examples include a rolling ball, a spinning coin, and a swinging pendulum.

Similar threads

  • Advanced Physics Homework Help
Replies
5
Views
831
  • Advanced Physics Homework Help
Replies
15
Views
1K
Replies
10
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
765
  • Introductory Physics Homework Help
Replies
4
Views
1K
Replies
2
Views
815
  • Advanced Physics Homework Help
Replies
14
Views
3K
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
552
  • Introductory Physics Homework Help
Replies
21
Views
1K
Back
Top