Mechanics II

Level 3 Physics Study: Angular Mechanics, Rotational Inertia, Angular Momentum, SHM, Resonance, Damping

d = rθ, where d = _______ displacement and θ = _______ displacement

linear, angular

linear displacement in measure in __

m

angular displacement is measured in ___

rad

360° = __rad = 1 revolution/rotation

2

ω = ∆d / ∆t, where ω = _______ ________

angular velocity

angular _______ is measured in rads^-1

velocity

angular ______ (rads^-1) = angular _______ (Hz)

velocity, frequency

ω = 2π__ = 2π/__, where ω = angular _______

f, T, frequency

angular frequency is measured in __

Hz

v = rω, where v = ________ velocity (ms^-1) and ω = _______ velocity (rads^-1)

linear, angular

α = ∆ω / ∆t = ra, where α = _______ acceleration (rads^-2) and a = ________ acceleration (ms^-2)

angular, linear

________ ________ is the gradient of a graph of angular displacement vs time

angular velocity

________ ________ is the gradient of a graph of angular velocity vs time

angular acceleration

________ ________ is calculated as the area under a graph of angular velocity vs time

angular displacement

rotational kinematics use the same equations as linear kinematics with the following substitutions:

d = ________ ________, θ

v = ________ ________, ω

a = ________ ________, α

________ stays the same!

angular displacement, angular velocity, angular acceleration, time

________ inertia is equal to ________, and is the resistance to the change of an object’s linear motion

linear, mass

linear inertia is measured in ___

kg

________ inertia, I, is ________ to mr², and is the resistance to a change in an object’s rotational motion

rotational, proportional

rotational inertia is measured in ____²

kgm

I = ∑m_ir_i², which can be summarised as I = __mr² where k = a ________

k, constant

k depends on an object’s shape and ________ ________, and 0 ≤ k ≤ 1

mass distribution

a ________ mass has the highest mass distribution, where k = 1

point

a solid ________ has a mass distribution of k = 2/5

sphere

the symbol for rotational inertia is __

I

rotational inertia is proportional to ________ ________, so an object with a greater mass distribution (all on one end) has a ________ (greater/smaller) rotational inertia

mass distribution, greater

________ means resistance to change

inertia

________ is required to provide angular acceleration

torque

________ is applied whenever a ________ is applied on an object which is not through the ________

torque, force, pivot

when an object is free to move in all directions, its ________ is located at its COM

pivot

τ = Fr, where r is the perpendicular distance from the line of action of the force to the ______ point

pivot

τ = Iα, where torque is proportional to both ______ ______ and ______ ______

rotational inertia, angular acceleration

torque is measured in __

Nm

______ rotational acceleration requires ______ to be additive but ______ to cancel out. this requires two thrusters with ______ in equal but opposite directions and ______ in the same direction

pure, torques, forces, forces, torques

1 thruster would not provide pure rotational acceleration as it would cause a/an ______ force, which would change the motion of the COM

unbalanced

I is the symbol for ______ ______ (kgm²)

rotational inertia

L is the symbol for ______ ______ (kgm²s^-1)

angular momentum

L = Iω, and angular momentum is ______ when there are no net external ______ acting on the system

conserved, torques

using conservation of angular ______, if rotational inertia decreases (due to a change in mass distribution), then angular velocity must ______

momentum, increase

for a satellite moving in an orbit, __ = mr² since a satellite is a ______ mass; and ω = __/r

∴ L = mvr, using only ______ quantities

I, point, v, linear

for ______ motion, E = ½mv²; for ______ motion, E = ½Iω², where mass has been substituted for ______ ______ and velocity has been substituted for ______ ______

linear, rotational, rotational inertia, angular velocity

______ kinetic energy is the ______ of both E_k(l______₎ and E_k(r______)

total, sum, linear, rotational

E_k for an object travelling in a/an ______ is considered either rotational or linear

orbit

a falling object may ______ gravitational potential energy and ______ both linear and rotational kinetic energy (gain/lose)

lose, gain