Understanding Rotational Motion: Answers for Jade

In summary, the equations provided show the relationship between the unit vector in the r direction and its change with respect to time. This change is represented by the angular speed, denoted by theta dot. Additionally, it is important to note that theta dot represents the change in angle of the unit vector.
  • #1
Jadenag
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Okay so my mechanics teacher is taking a rather mathematical approach to CM and its really confusing me. Can someone explain to me what this actually means?

d hat{r}/dt=dot{theta} hat{theta} and

d hat{theta}/dt=-dot{theta} hat{r}

I mean I know that anything with a hat on top is a unit vector and i also know that theta dot represents angular speed. Thankyou.

-jade
 
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  • #2
Hi Jadenag! :smile:

Jadenag said:
Okay so my mechanics teacher is taking a rather mathematical approach to CM and its really confusing me. Can someone explain to me what this actually means?

[itex]{d \hat{r} \over dt}=\dot{\theta} \hat{\theta}[/itex] and

[itex]{d \hat{\theta} \over dt}=-\dot{\theta} \hat{r}[/itex]

I mean I know that anything with a hat on top is a unit vector and i also know that theta dot represents angular speed. Thankyou.

-jade

Yes, [itex]\hat r[/itex] is the local unit vector in the r direction at some point (r, theta).
We could also write [itex]\hat r(r, \theta)[/itex], since it is a function of r and theta.
However, if theta increases a little bit (by [itex]d\theta[/itex]), that unit vector changes.
To be precise its angle changes by [itex]d\theta[/itex].

Perhaps you can make a drawing of it and consider which vector represent the change in [itex]\hat r[/itex]?
 

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. It is different from linear motion, which is movement in a straight line.

2. What are some common examples of rotational motion?

Some common examples of rotational motion include the spinning of a top, the rotation of a wheel, the swinging of a pendulum, and the spinning of the Earth on its axis.

3. How is rotational motion measured?

Rotational motion is measured in radians, which is a unit of angular measurement, or degrees, which is a unit of circular measurement. It can also be measured using the rotational speed or angular velocity of an object.

4. What factors affect rotational motion?

The main factors that affect rotational motion are the mass of the object, the distance between the object and its axis of rotation, and the force applied to the object. Other factors include the shape and size of the object, as well as any external forces such as friction or air resistance.

5. How does rotational motion relate to linear motion?

Rotational motion and linear motion are closely related. In fact, rotational motion can be thought of as a type of circular linear motion. This means that the same principles of motion, such as velocity, acceleration, and force, apply to both types of motion.

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