#11.1.1
Concept of moment of inertia
\(I = mr^2 \) for a point mass.
\(I = Σmr^2 \) for an extended object.
Qualitative knowledge of the factors that affect the moment of inertia of a rotating object.
Expressions for moment of inertia will be given where necessary.
#11.1.2
Rotational kinetic energy
\(E_k = \dfrac{1}{2}Iω^2 \)
Factors affecting the energy storage capacity of a flywheel.
Use of flywheels in machines.
Use of flywheels for smoothing torque and speed, and for storing energy in vehicles, and in machines used for production processes.
#11.1.3
Rotational motion
Angular displacement, angular speed, angular velocity, angular acceleration,
\(ω = \dfrac{∆θ}{∆t} \), \(α = \dfrac{∆ω}{∆t} \)
Representation by graphical methods of uniform and non-uniform angular acceleration.
Equations for uniform angular acceleration;
\(ω_2 = ω_1 + αt\), \(θ = \Big(\dfrac{ω_1+ω_2}{2}\Big)t \)
\(θ = ω_1t + \dfrac{αt^2}{2} \), \(ω_2^2 = ω_1^2 + 2αθ \)
Students should be aware of the analogy between rotational and translational dynamics.
#11.1.4
Torque and angular acceleration
\(T = Fr\)
\(T = Iα\)
#11.1.5
Angular momentum
\(\text{angular momentum} = Iω \)
Conservation of angular momentum.
Angular impulse = change in angular momentum;
\(T∆t=∆(Iω) \) where T is constant.
Applications may include examples from sport.
#11.1.6
Work and power
\(W = Tθ \); \(P = Tω \)
Awareness that frictional torque has to be taken into account in rotating machinery.