Rotational-Quantities General Physics 1 Q2.ppt

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1. Rotational
Quantities

2. 2
Describe rotational quantities using
vectors. ( STEM_GP12REDIIa-4)
MELC

3. 3
Background information for
the Learners

Translation is the motion along a
straight line, while rotation is the
motion requiring an object to rotate
about its fixed axis.

Table 1.Translational quantities and
their equivalence in rotational
motion.

4. 4
Translation Rotation
Quantity Symbol Symbol Quantity
Position x or y θ Angular
Position
Displacement Δx or Δy Δθ Angular
Displacement
Velocity v ω Angular
Velocity
Acceleration a α Angular
Acceleration
Mass or Inertia m I Moment of Inertia

5. 5
Translation Rotation
Quantity Symbol Symbol Quantity
Force F ԏ Torque
Linear p L Angular
Momentum Momentum
Work Fd ԏθ Work
Kinetic ½ mv
2
½ I ω
2
Rotational
Energy Kinetic energy
Power Fv ԏω Power

6. 6
Basic Rotational Quantities
Angular position is the angle through
which a point revolves around a
center or through which line has
been rotated about a specified axis.
Its value is positive when the
rotation is counterclockwise and
negative when the rotation is
clockwise.

7. It is defined by: θ=s/r
where: θ is the angular position.
s- is the length of arc along a circle
r- is the radius of the circle
•The SI unit for angular position is
radian.
•Take note that one revolution in a
circle equals 2π radians or 360º.

8. 8

9. 9
The angular displacement is the change in
the angular position of the
rotating object. In symbols:
Δθ =
??????
2 −
??????
1
where Δθ is angular displacement (Δ is
read as delta meaning change)
??????
2 − is final angular position
??????
1 − is initial angular position

10. 10
▪ If the initial angular position is the
zero angular position, then angular
displacement is equal to angular
position.
▪ Angular displacement is also
measured by radians.
▪ It is positive for counterclockwise
rotation and negative for clockwise
rotation.

11. The angular velocity is the rate of
change in angular position.
Mathematically, it is described as:
∆?????? ??????2 - ?????? 1
∆?????? ??????2 - ??????1
where ω is angular velocity (ω is
read as omega)

12. 12
Δθ is change in angular position
Δt is change in time

The SI unit for angular velocity is
radians/second (rad/s).
But then we also encounter other
unit – rpm, meaning revolutions per
minute.

13. The direction of angular velocity is
defined by right-hand rule: Curl your
right hand about the rotating object.
Your fingers are pointing in the
direction of rotation, and your
extended thumb points in the direction
of angular velocity (see figure 2).
Similarly, it is positive for
counterclockwise rotation and
negative for clockwise rotation.

14. 14

15. 15
▪ The angular acceleration is the
change in angular velocity per unit
time.
▪ Its direction is the same with angular
velocity if and only if the rotation
increases in speed.
▪ But when the rotation is slowing
down, its direction is opposite of the
angular velocity’s direction.
It is measured in radians per squared
seconds (rad/s
2
).

16. 16
In symbols, it is defined as:
∆?????? ?????? 2 - ??????1
∆?????? ?????? 2 - ??????1
where ?????? is the angular acceleration
Δω is change in angular velocity
Δt is change in time
These basic quantities have both
magnitude and directions, then they
are vectors.

17. 17
▪These basic quantities have both
magnitude and directions, then they
are vectors.
▪However, a vector in pure rotation
defines only the axis of rotation and
not a direction in which the object
moves.
▪Hence, we can describe these
rotational quantities as either positive
or negative.