Flashcards in Unit 5: Rotational dynamics Deck (58)
What are angles and angular displacements measured in?
What is the definition of a radian?
When the arc length is equal to the radius, the angle θ is equal to one radian
What is the formula for angular velocity?
ω = Δθ/Δt rad(s^-1)
What is the formula for velocity in terms of angular velocity?
v = rω
When does angular acceleration arise?
When a particle increases its speed of rotation
What is angular acceleration defined as?
The rate of change of angular velocity
What is the formula for angular acceleration?
α = Δω/Δt rad(s^-2)
What must an increase in angular acceleration be accompanied by?
A corresponding increase in the tangential acceleration
What is the formula for tangential acceleration in terms of angular acceleration?
a = rα
What do the dynamics involving movement about a circle assume?
It considers a body that can be treated as a single particle where all the mass is centred at a point but this simplistic assumption cannot be made in more realistic situations
What does the dynamics of a rotating body depend upon?
The distribution of the mass of the body in relation to a particular axis of rotation
What is a body composed of?
An infinite number of point masses (or elemental particles) that move collectively - each point mass within the body will have a different radius from the axis of rotation and will therefore rotate with a different tangential velocity
What does inertia mean?
The resistance of an object to a change in its motion
What is the formula for the moment of inertia?
I = Σm(r^2)
What are the units of the moment of inertia?
When is the summation for the moment of inertia replaced by integration?
In the case of a rigid body with a mass that is continuous
What affects the value of the moment of inertia?
The precise location of the axis of rotation
What increases the moment of inertia?
Distributing the mass further from the centre of rotation
What is the moment of inertia of a hoop about the central axis?
I = M(R^2)
What is the moment of inertia of a solid sphere about any diameter?
I = 0.4M(R^2)
What is the moment of inertia of a solid cylinder/disc about the central axis?
I = 0.5M(R^2)
What happens to the moments of inertia of two objects that share a common axis of rotation?
Their individual moments of inertia are added together to give a moment of inertia for the combined system
What is a flywheel?
A mechanical device with a large moment of inertia that stores rotational energy
What is the formula for rotational kinetic energy?
Ek = 0.5I(ω^2)
When a body is rotating about a centre of rotation, what does it possess energy due to?
Its rotational movement
What are the four rotational equations of motion?
ω2 = ω1 + αt, θ = ω1t + 0.5α(t^2), (ω2)^2 = (ω1)^2 + 2αθ and θ = 0.5(ω1 + ω2)/t
What is torque?
The moment (or turning effect) of a force about a point
What is the definition of torque?
A torque is the product of a force and the perpendicular distance of the line of action of the force from a perpendicular point of rotation. The unit of torque is newton metre (Nm). The convention adopted is that positive torques produce a clockwise rotation
What is the formula for torque in terms of force?
T = Fs