# Unit Planner: Rotational dynamics

Unit: Rotational dynamics

Start date:

**Diploma assessment**

*When will the content be assessed?*

*Paper 1Paper 2Paper 3 xInvestigation x*

**Text book reference**

Hamper - online resources

#### Inquiry: Establishing the purpose of the unit

**Transfer Goals***List here one to three big, overarching, long-term goals for this unit. Transfer goals are the major goals that ask students to “transfer”, or apply, their knowledge, skills, and concepts at the end of the unit under new/different circumstances, and on their own without scaffolding from the teacher. *

- To know the concepts of moment of inertia, angular velocity, torque and angular momentum
- To understand the effects of work done on rotating bodies
- To be able to predict the equivalent rotational and translational dynamics equations

**Content***List here the key content that students will know by the end of the unit *

__Rotation__

- State the definition of Torque and understand their effect.
- State the conditions for equilibrium.

__Torques and angular acceleration__

- Define angular displacement, velocity and acceleration.

__Angular momentum__

- Define angular momentum.
- State the principle of conservation of angular momentum.

**Skills***List here the key skills that students will develop by the end of the unit. *

__Rotation__

- Use the conditions for equilibrium to solve problems involving balanced beams and masses.

__Torques and angular acceleration__

- Solve problems where forces and torques must be balanced.
- Solve problems involving forces that are not perpendicular to line joining point of application to pivot.
- Solve problems using the angular suvat equivalents.

__Newton's Second Law and rotation__

- By considering a rigid body to be made of a number of points, derive the equation Γ = Σmr
^{2}. - Solve problems related to angular acceleration and Torque for bodies ok known moment of inertia.

__Rotational kinetic energy and work__

- Derive equation KE = 1/2 Iω
^{2}by considering the KE energy of individual particles of a rigid body. - Derive W = Γθ by considering the work done by small displacments of a rotating force.
- Calculate the KE gained when a torque is applied to a rigid body.
- Derive the equation for the final velocity of a ball rolling down a slope.

__Angular momentum__

- Apply the principle of angular momentum to explain different examples and solve problems.

**Concepts***List here the key concepts that students will understand by the end of the unit*

__Rotation__

- Understand that bodies can rotate if a force doesn't act on the centre of mass.
- Understand that unbalanced torques will cause rotation.
- Understand how balancing torques can be utilised in levers.

__Newton's Second Law and rotation__

- Understand the relationship between tangential motion and rotational motion (v = ωr, a = αr)
- Understand how by applying Newton's 2nd law to the tangential motion of a particle moving in a circle we find that Γ = mαr
^{2}. - Understand how the moment of inertia is related to the way mass is distributed around the pivot.

__Rotational kinetic energy and work__

- Understand why a rolling ball gets down a slope slower than a sliding one.

**Applications***Examples of real world practical applications of knowledge. *

- This whole topic "engineering physics" is one big utilisation. Advances in engineering have certainly changed the way we live but not all communities have been affected to the same extent.
- Levers
- Cantilevers
- Bridges
- Leaning ladders
- Pub signs
- Traction engine flywheels
- Tightrope walker poles
- Ice skating
- Gymnastics
- Diving
- Break dancing
- Physics teachers sitting on revolving chairs

#### Action: teaching and learning through Inquiry

**Approaches to teaching***Tick boxes to indicate pedagogical approaches used. *

*Lecture x*

Simulation x

Small group work (pairs) x

Hands on practical x

Video x

Simulation x

Small group work (pairs) x

Hands on practical x

Video x

*Student centred inquiry x*

**TOK***Examples of how TOK can be introduced in this unit *

- In Interactive Physics we can apply parallel forces to a body in space. This gives an unexpected results since we imagine the outcome in the gravitational field of the Earth.
- What is the difference between engineering and physics?
- Angular momentum is not so intuitive as linear momentum. It is relatively easy to visualise the outcome of two balls colliding but not so simple to visualise a mass landing on a rotating platform.
- When children play on a roundabout they experience the effect of changing the moment of inertia but how many realise that it spins faster if everyone moves to the centre?

**NOS***Examples of how NOS can be introduced in this unit. *

- Up to this point in the course we have been considering bodies to be points. This model is not enough to solve problems involving rigid bodies so we define some new quantities.
- Interesting how the angular quantities are related in the same way so lead to the same equations.
- We have developed Newton's second law for examples of constant linear acceleration. By taking small steps, where the acceleration is considered constant, we can apply it to rotational problems.
- When doing the rolling ball practical earlier in the year there were certain things that couldn't be explained. Now they can be.

**Assessments***Tests, exams and marked labs*

**Worksheets and exercises**

**Resources***Video clips, simulations demonstrations etc*.

- Introduction to rotation
- Optional Practical: Measuring moment of Inertia
- Torques and angular acceleration
- Optional Practical: Balanced beam (Geogebra)
- Optional Practical: Rotational dynamics (Algodoo)
- Optional Practical: Rubber powered motor
- Optional Practical: Meccano
- Newton's 2nd law and rotation
- Optional Practical: Rolling cylinders (Algodoo)
- Rotational KE and work
- Angular momentum
- Optional Practical: Conservation of angular momentum (Algodoo)

#### Reflections

**What went well***List the portions of the unit (content, assessment, planning) that were successful *

**What didn’t work well***List the portions of the unit (content, assessment, planning) that were not as successful as hoped *

**Notes/changes/suggestions:***List any notes, suggestions, or considerations for the future teaching of this unit*.