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5.2 Connecting Rotational to Linear Kinematics

Section 1 of 2

Linear Motion in Rotational Motion

Interactive Content
Note: All content in this lesson is interactive. Hover over the glowing blue terms to learn more about a Vocabulary term. Hover over the icons to learn more about a Key Formula or Graph. Hover over any line, point, or curve on any graph or diagram to learn more about it.

In rotational motion, objects rotate around an axis. While this can be described as a rotational motion, you can also see that any point along the object will also be moving linearly in a circle. The distance between the point and the axis of rotation is represented with the variable

r{r}
.

By definition of the radian, the linear position (
Δs{\Delta s}
) that a point moves when it is rotated is equal its distance from the axis (
r{r}
) multiplied by the angular displacement (
Δθ{\Delta \theta}
), which gets the equation:
Δs=rΔθ{\Delta s=r \Delta \theta}
. From this derivation, we can derive many more relationships, such as
s=rθ{s=r \theta}
,
v=rω{v=r \omega}
, and
a=rα{a=r \alpha}
.

MCQ Reading Checkpoint

When a sphere is rolling with a constant angular speed, if its radius is increased with its angular speed kept constant, the sphere will...

Choose the best option:
A

Have a higher angular acceleration

B

Have a higher linear velocity

C

Have a lower angular acceleration

D

Have a lower linear velocity
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