4/13/2026
Rectilinear Motion vs. Curvilinear Motion
CIRCULAR
MOTION
Prepared by: Engr. Gabriel Galvez
3rd Term SY 2025-2026
Uniform Circular Motion
- Constant Speed
- Different Velocity
Aspect
Rectilinear Motion
Curvilinear Motion
Definition
Motion along a straight line
Motion along a curved path
Path
Linear (straight)
Curved (circular, parabolic, etc.)
Dimensions
One-dimensional (1D)
Two- or three-dimensional (2D/3D)
Direction
Constant direction (may reverse but
still straight)
Continuously changing direction
Velocity
Changes only in magnitude (if
accelerating)
Changes in both magnitude and
direction
Acceleration
Along the same straight line
Has components (e.g., tangential and
normal)
Complexity
Simpler to analyze
More complex (requires vector
analysis)
Examples
Car on a straight road, free-falling
object
Projectile motion, circular motion,
curved road
Uniform Circular Motion
Quantity
Direction
𝑑𝜃
𝑑𝑡
𝑣 = 𝑟𝜔
Centripetal
Acceleration
Toward center
𝑎𝑛 =
Tangential
Acceleration
Along tangent
𝜔=
Total Acceleration
Centripetal Force
Quantity
Formula/ Definition
Period (T)
𝑡ℎ𝑒 𝑡𝑖𝑚𝑒 𝑓𝑜𝑟 𝑜𝑛𝑒 𝑐𝑦𝑐𝑙𝑒 𝑡𝑜 𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑒
(seconds/cycle)
1
𝑓=
𝑇
(Hertz = Hz)
2𝜋𝑟
𝑣𝑎𝑣𝑒 =
𝑇
2𝜋𝑟 2𝜋𝑟 2𝜋
𝑇=
=
=
𝑣𝑎𝑣𝑒
𝑟𝜔
𝜔
𝜔
𝑓=
2𝜋
Velocity Average in terms of T
Period in terms of Vave
Frequency in terms of 𝜔
𝑎𝑡 = 𝑟𝜃
𝑎=
Toward Center
𝑣2
𝑟
𝑎𝑡2 + 𝑎𝑛2
𝑚𝑣 2
𝐹=
𝑟
Note:
- Tangential Acceleration can be
calculated using “constant
acceleration” formulas and it is
always constant.
Example 4.1
Other Parameters
Frequency (f)
Formula
Tangential Velocity Tangent to circle
Angular Speed
Find the centripetal acceleration for a point on the equator of
the earth. Given the radius of the earth = 6.37x10^6m and the
period of rotation for the earth is 1 day.
1
4/13/2026
Example 4.2
Example 4.3
A planet orbits a sun in a uniform circular orbit
(r=3.6x10^7m). The centripetal acceleration is 10% of the
earth’s gravitational acceleration. How fast is it moving and
how long is a “half a year”?
A racecar, moving at a constant tangential speed of 60 m/s,
takes one lap around a circular track in 50 seconds.
Determine the magnitude of the acceleration of the car.
Example 4.4
Example 4.5
An object that moves in uniform circular motion has a centripetal
acceleration of 13 m/s2. If the radius of the motion is 0.02 m, what is
the frequency of the motion?
The racing car shown in the figure is traveling at 90 kph
when it enters a semicircular curve at A. The driver increases
the speed at a uniform rate, emerging from the curve at C at
144 kph. Determine the:
a) Tangential acceleration when the car is at B.
b) Normal acceleration when the car is at B.
c) Total acceleration when the car is at B.
2