1. TYPES OF MOTION

2. TRANSLATION (or linear) – motion along a path; measureable quantities include both position and velocity

3. ROTATIONAL – spinning at a constant rate about a vertical axis

4. CIRCULAR – set of motion along an orbit

5. about an external point
object moves in
circular path
about an external point
(“revolves”)

6. According to Newton’s First Law of Motion,
objects move in a straight line unless a force
makes them turn. An external force is necessary
to make an object follow a circular path.
This force is called a
CENTRIPETAL (“center seeking”) FORCE.
Since every unbalanced force causes an object
to accelerate in the direction of that force
(Newton’s Second Law), a centripetal force
causes a CENTRIPETAL ACCELERATION. This
acceleration results from a change in direction,
and does not imply a change in speed,
although speed may also change.

7. v = 2pr/T v r m gravity - planets orbiting the sun
Centripetal force and acceleration may be caused by:
gravity - planets orbiting the sun
friction - car rounding a curve
a rope or cord - swinging a mass on a string
In all cases, a mass m moves in a circular path
of radius r with a linear speed v. The time to make
one complete revolution is known as the period, T.
The speed v is the
circumference divided by the period. v r m
v = 2pr/T

8. ac = v2/r Fc = mac = mv2/r and centripetal force (Fc) is:
The formula for centripetal acceleration (ac) is:
ac = v2/r
and centripetal force (Fc) is:
Fc = mac = mv2/r
m = mass in kg
v = linear velocity in m/s
Fc = centripetal force in N
r = radius of curvature in m
ac = centripetal acceleration in m/s2

9. (“rotates” or “spins”)
object moves in
circular path about
an internal point
or axis
(“rotates” or “spins”)

10. degrees, radians, or rotations. deg/s, rad/s, rpm, etc...
The amount that an object rotates is its
angular displacement.
angular displacement, q, is given in
degrees, radians, or rotations.
1 rotation = 360 deg = 2p radians
The change in an object’s
angular displacement over time is its
angular velocity.
angular velocity, w, is given in
deg/s, rad/s, rpm, etc...

11. The change in an object’s angular velocity over time is its
angular acceleration.
Angular acceleration, a, is given in
deg/s2, rad/s2, rpm/s, etc...
Formulas for rotational motion follow an
exact parallel with linear motion formulas.
The only difference is a change in variables
and a slight change in their meanings.

12. TRANSLATIONAL (LINEAR) AND
ROTATIONAL FORMULA
TRANSLATIONAL
ROTATIONAL
wf = wi + at
vf = vi + at
q = wavt
d = vavt
ωav= (wf + wi)/2
vav = (vf + vi)/2
d = vit + ½ at2
q = wit + ½ at2
vf2 = vi2 + 2ad
wf2 = wi2 + 2aq