Lesson Plan
Session title
Rotational inertia
Date
Dec. 10th
Location
Room 402
Learner group
Grade 11 AP
Duration
40 minutes
Group size
10
Learning aims
Cultivate the students’ ability to analyse and solve problems is physics using Calculus.
A statement which provides the scope of the
subject and the overall intent of the course
Learning objectives
What are learners expected to learn after
completing the lesson? These should be
specific and able to be assessed.
By the end of the lesson students will be able to:
1.
Calculate the moment of inertia of point masses that are located in a plane about an axis perpendicular to the plane.
2.
Explain the differences in the moments of inertia between different objects such as rings, discs, spheres, or other regular shapes by
applying the general definition of moment of inertia (rotational inertia) of a rigid body.
3.
Calculate by what factor an object's rotational inertia will change when a dimension of the object is changed by some factor.
4.
Derive the moment of inertia, using calculus, of a thin rod of uniform density about an arbitrary axis perpendicular to the rod.
5.
Derive the moments of inertia for a thin cylindrical shell about its axis or an object that can be considered to be made up of coaxial
shells.
Inclusion
How will you make your lesson inclusive?
Lesson plan template
Simple parts of the lesson will be delivered in English. Local teacher will explain some challenging concepts in Chinese.
Lesson Plan
Time
10 minutes
Donna
(Ruslan write
the students
answer to the
black board)
7 minutes
Ruslan
(Donna checks
students
understanding)
1 minute
Donna
What are you doing?
What are your students doing?
Introduce new physical quantity “Rotational Inertia” using the equation of
kinetic energy.
Define rotational inertia as a measure of a body's resistance to angular
acceleration.
Q1: What is the equation of kinetic energy of a particle?
Q2: What does link angular and linear velocity?
Show the definition of the rotational inertia by equation on ppt. (For a single
particle it’s equal to the product of the mass of a particle and the square of its
distance from an axis of rotation.)
Q3: If the r is increased by two times, how will its rotational inertia change?
(Learning Objective 3)
High light what is r in the equation. Show pics on ppt of a person in different
posture, explain which one has bigger inertia.
Q4: There is a ring and a disc with same mass. Which one has bigger inertia?
(Learning Objective 2)
For a system of particles: The sum of the products of each mass element of a
body multiplied by the square of its distance from an axis.
Explain how to find rotational inertia of a system of point objects with different
masses located in a plane about an axis y, z, and x.
Problem about a system of two pair of balls located at equal distance to axis of
rotation. (In handout)
State: changing the axis of rotation of an object changes its rotational inertia
because of the different mass distribution.
(Learning Objective 1)
𝑀
Give the definition of linear density: 𝜆 =
Listen carefully, take notes and answer the questions.
A1:
𝑚𝑣 2
𝐸=
2
A2:
𝑣 = 𝜔𝑟
Make notes
Area density: 𝜎 =
𝐴
Volume density: 𝜌 =
10 minutes
Ruslan
(Donna
supports and
checks
students
understanding)
𝐿
𝑀
Listen carefully, take notes.
Solve the problem.
Take notes
𝑀
𝑉
Explain that for calculation rotational inertia of continuous solid body Calculus
is necessary. Explain how to calculate rotational inertia of a homogeneous thin
rod about an axis at one end using Calculus.
Show the students first two steps:
𝐼 = ∫ 𝑑𝐼
𝑑𝐼 = 𝑥 2 𝑑𝑚
Q1: what is x?
Q2: where is dm?
Q3: how to use linear density 𝜆 and dx to represent dm?
Ask the students to finish the math themselves.
(Learning Objective 4)
Lesson plan template
A3: It will increase 4 times.
A4: Ring has bigger inertia.
Listen carefully, take notes.
A1: distance x from an axis of rotation
A2: the tiny mass has a distance of x from the axis of
rotation
A3: 𝑑𝑚 = 𝜆𝑑𝑥
Solve the problem.
Learning materials and
resources
Presentation, handouts
Lesson Plan
Time
10 minutes
Donna
What are you doing?
Explain how to calculate rotational inertia of a homogeneous solid cylinder
considering that it’s made up of coaxial thin shells.
Show the first two steps with the students:
𝐼 = ∫ 𝑑𝐼
𝑑𝐼 = 𝑥 2 𝑑𝑚
Q1: what is x?
Q2: where is dm?
Q3: how to use volume density 𝜌 and dx to represent dm?
Ask the students to finish the math themselves.
Q4: if it is a cylinder shell, how to make necessary changing?
(Learning Objective 5)
3 minutes
Summarize the lesson
Ruslan
Q1: What is the rotational inertia equal to?
Q2: Why changing the axis of rotation of an object changes its rotational
inertia?
Use as many rows in the table as applicable – add rows if necessary
Lesson Evaluation: Include what you feel went well and what you would like to improve.
Lesson plan template
What are your students doing?
Listen carefully, take notes.
A1: distance x from an axis of rotation
A2: the tiny mass has a distance of x from the axis of
rotation
A3: 𝑑𝑚 = 𝜌𝑑𝑉 = 𝜌(2𝜋𝑥𝐿)𝑑𝑥
A4: change the upper limit and the lower limit of the
integral
Answer the questions.
Ask the questions.
Learning materials and
resources