General Physics I - Moment of Inertia.pdf

General Physics I - Moment of Inertia.pdf

1. Moment of Inertia
Physics I

2. Have you ever tried
spinning a broom? Is it
easier when you hold it at
the middle or at the end?

3. Have you ever tried
spinning a basketball on
your finger? Why do you
think sometimes it is easy
and sometimes it is hard?

4. Activity 1: Spin the Bottle Experiment
Objective: To observe how mass
distribution affects spinning (moment
of inertia).

5. Activity 1: Spin the Bottle Experiment
Materials:
2 bottles same size ( one is empty, one
is filled with water or sand)

6. Activity 1: Spin the Bottle Experiment
Procedures:
1.First, place both bottles on the floor
or on your desk
2.Spin the empty bottle with your hand.

7. Activity 1: Spin the Bottle Experiment
Procedures:
3. Now, spin the filled bottle in the
same way.
4. Observe which one is easier to spin
and which one stops faster.

8. Activity 1: Spin the Bottle Experiment
Guide Questions:
1. Which bottle is lighter to spin?
2. Which bottle is harder to spin and
keeps moving longer?

9. Activity 1: Spin the Bottle Experiment
Guide Questions:
1. Which bottle is lighter to spin?
-The empty bottle.
2. Which bottle is harder to spin and keeps
moving longer?
-The filled bottle.

10. Activity 1: Spin the Bottle Experiment
Guide Questions:
3. Which one has a bigger resistance to spinning, and
why do you think so?
-The filled bottle is harder to spin because it has more
mass.
-The empty bottle spins easily because it is lighter.

11. Moment of inertia

12. Moment of inertia
-is the amount of resistance an
object has to being made to spin.
Think of it like ‘spin heaviness’
-the more spin-heaviness, the
harder it is to start or stop
spinning.

13. Introduce the important
words

14. Moment of inertia
1.Axis — the line an object spins
around (draw a vertical line or a
dot labeled ‘axis’).
2.Mass (m) — how much stuff is in
the object (kg).

15. Moment of inertia
3. Radius / distance (r) — how far
the mass is from the axis (meters).
4. Moment of inertia (I) — how
hard it is to spin that mass about
the axis.

16. Moment of inertia
FORMULA:
I = m r²
For a small object (a point mass) at distance r from
the axis, we multiply its mass m by the square of
its distance r². That number (I) tells us the
spin-resistance. If there are many small masses,
we add each one’s m r².

17. The two things that make I big or
small
1.If the mass m is bigger (more
mass), I gets bigger → harder
to spin.

18. The two things that make I big or small
2. If the mass is farther from the axis
(r bigger), I grows a lot because r is
squared. That means moving mass a
little farther out makes it much harder
to spin, this is why figure skaters pull
in their arms to spin faster.

19. The two things that make I big or small
2. If the mass is farther from the axis
(r bigger), I grows a lot because r is
squared. That means moving mass a
little farther out makes it much harder
to spin, this is why figure skaters pull
in their arms to spin faster.

20. Problem ( Single object)
Formula: I = m r²
1.A 2.00 kg mass is 0.50 m from the axis. Find I.
r² = 0.50 × 0.50 = 0.2500 (0.50 squared = 0.25).
Multiply by mass: I = 2.00 × 0.25.
I = 0.50 kg·m²

21. Problem ( Two equal masses)
Formula: I = m r²
2. Two objects, each with mass 1.00 kg, are each 1.00
m from the axis (on opposite sides). Find total I.
I = mr² = 1×(1)²=1
I total = 1+1 = 2
I total = 2.00 kg·m²

22. Problem ( Two different masses)
Formula: I = m r²
3. Mass A = 3.0 kg at r₁ = 0.20 m; Mass B = 1.5 kg at
r₂ = 0.80 m. Find I total.
Given:
Mass A = 3.0 kg at r₁ = 0.20 m
Mass B = 1.5 kg at r₂ = 0.80 m

23. Problem ( Two different masses)
Formula: I = m r²
Mass A:
r² = 0.20 × 0.20 = 0.04
I1 = 3.0×0.04=0.12









Mass B:

r² = 0.80×0.80=0.64

I2 = 1.5×0.64 = 0.96

Itotal = I1 + I2 = 0.12 + 0.96 = 1.08kg kg·m²
Itotal = 1.08kg kg·m²

24. ACTIVITY: SOLVE THE FOLLOWING
PROBLEMS:
1.A 4.0 kg mass is 0.30 m from the axis. Find I.
2.A 1.5 kg mass is 0.75 m from the axis. Find I.
3.A 0.80 kg mass is 1.20 m from the axis. Find I.
4.A 5.0 kg mass is 0.10 m from the axis. Find I.
5.Two 2.0 kg objects are each 0.50 m from the axis (on
opposite sides). Find Itotal.
6.Two 3.0 kg objects are each 1.0 m from the axis. Find
Itotal.

25. ACTIVITY: SOLVE THE FOLLOWING
PROBLEMS:
7. Two 0.5 kg objects are each 0.20 m from the axis. Find
Itotal.
8. Mass A = 2.0 kg at r₁ = 0.40 m; Mass B = 1.0 kg at r₂ =
0.60 m. Find Itotal.
9. Mass A = 4.0 kg at r₁ = 0.10 m; Mass B = 2.0 kg at r₂ =
0.80 m. Find Itotal.

26. ACTIVITY: SOLVE THE FOLLOWING
PROBLEMS:
10. Mass A = 1.5 kg at r₁ = 0.25 m; Mass B = 3.5 kg at
r₂ = 0.75 m. Find Itotal.

27. Thank
You.