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Level 89

Rotational Motion & Equilibrium


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rotational speed (units)
revolutions per unit of time
Nm
torque (units)
kg (m^2)
moment of inertia (units)
rad/s
angular speed (units)
kg (m^2/s)
angular momentum (units)
rad/s^2
angular acceleration (units)
π/180
to convert degrees to radians, multiply it by . . . ?
180/π
to convert radians to degrees, multiply it by . . . ?
57.3
about how many degrees are in one radian?
ω=(∆θ)/(∆t)
formula for angular speed
τ=Fl
formula for torque
θ=ωit+(αt^2)/2
formula for angular displacement
ωf^2=ωi^2+2αθ
formula to find final or initial angular speed, angular acceleration, or angular displacement
α=(∆ω)/(∆t)
formula for angular acceleration
xcm=(x1m1+x2m2...)/(m1+m2...)
formula for the center of mass (x-coordinate)
.372
if a sphere travels 14 m and its radius is 6 m, then how many revolutions does it make along the way, rounded to three decimal places?
halfway between both their centers of mass
if 2 blocks with uniform mass are placed on top of each other, with the second's left edge touching the center of the first's so that it comes off it on the right mildly, w…
90
at what angle is torque greatest?
L=Iω
formula for angular momentum
I=mr^2
moment of inertia for hoop/cylindrical shell
I=2(mr^2)/3
moment of inertia for hollow sphere
I=3(mr^2)/2
moment of inertia for disk/solid cylinder (axis at rim)
I=(mr^2)/2
moment of inertia for disk/ solid cylinder (axis at center, normal)
I=2(mr^2)/5
moment of inertia for solid sphere
I=(m[length^2])/12
moment of inertia for long thin rod (axis through midpoint)
I=(m[length^2])/3
moment of inertia for long thin rod (axis at one end)
I=(m/12)(length^2+width^2)
moment of inertia for solid plate (axis perpendicular to plane of plate)
KE=(Iω^2)/2
kinetic energy of a rotating object
τ=Iα
formula indicating relationship between torque and angular acceleration
2rω
the velocity of the top of a wheel that rolls without slipping
the velocity at the middle of a wheel that rolls without slipping
0
the velocity at the bottom of a wheel that rolls without slipping