A child is playing with a 2.00 kg spinning toy (yo-yo) consisting of an axle connected to two disks, and a string looped around the axle, as shown below. The toy moves up and down as the toy winds and unwinds the string. It has a moment of inertia I = 2.72 X 10-4 kg-m2. At the time shown below, the toy is rotating with an angular speed w = 29.2 rad/s. The string is wound around the axel, whose radius is 2.50 cm. Find the total kinetic energy (rotational plus translational) of the toy as it moves up the string at that point.
A child is playing with a 2.00 kg spinning toy (yo-yo) consisting of an axle connected to two disks, and a string looped around the axle, as shown below. The toy moves up and down as the toy winds and unwinds the string. It has a moment of inertia I = 2.72 X 10-4 kg-m2. At the time shown below, the toy is rotating with an angular speed w = 29.2 rad/s. The string is wound around the axel, whose radius is 2.50 cm. Find the total kinetic energy (rotational plus translational) of the toy as it moves up the string at that point.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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A child is playing with a 2.00 kg spinning toy (yo-yo) consisting of an axle connected to two disks, and a string looped around the axle, as shown below. The toy moves up and down as the toy winds and unwinds the string. It has a moment of inertia I = 2.72 X 10-4 kg-m2. At the time shown below, the toy is rotating with an angular speed w = 29.2 rad/s. The string is wound around the axel, whose radius is 2.50 cm. Find the total kinetic energy (rotational plus translational) of the toy as it moves up the string at that point.
Transcribed Image Text:Area of circle: A = Tr?
Rate of flow
Q = Av
t = F(sin0)r
T = Fl, wherel= lever arm
Bernoulli's equation:
1
P+
+ pgy, = P, +
1
pv,´ + pgy,
Equilibrium:
Te = T - 273.15°C
Στ=0
9
T =
-T. +32
5
Non-equilibrium:
5
Tc =-(T, - 32)
Στ= Ια
Тетреrature:
Moment of inertial for a point mass
revolving about a center at a distance r:
ΔL L,ΔΤ
AA = y A,AT Y = 2a
AV = BVAT B = 3a
I= Mr?
Kinetic Energy:
Specific Heat:
Translational: ½ mv²
Rotational: ½ Im?
(J/kg. 'C)
mAT
Q = mc(T, –T,)
Angular speed o =v/r
Qcold
=-Qhot
Tensile strain:
EQ = 0
Latent Heat:
F
AL
L.
Y -Young's modulus
phase change: Q=±mL
Energy Transfer:
ΔΤ
P =
At
Density:
Ar
M
p =
V
(kg/m²)
Thermal conductivity:
Pressure:
(T, – T.)
P = kA
L.
F
P=
A
(Ра)
Hooke's Law:
F =-kx
P = P, + pgh
Acceleration in simple harmonic
motion:
Archimedes' principle:
k
a =
B = P fuidV fa
m
fluid8
Elastic potential energy:
РЕ, %3D
-kx²
2
Equation of flow continuity:
Av, = A,v,
Period:
Transcribed Image Text:Intensity level:
m
T = 2n,
k
B=10log
I.
Frequency:
f =
T
Intensity level difference:
Angular frequency:
k
w = 2n f
AB =10log
I,
m
PV = nRT, where R = 8.31 J/mole-K
Maximum Velocity, Acceleration:
A2n f
Ao = A(2nf}
Umax = A@ =
a max =
PV = constant,
PIV1 = P2V2
A = (27 f)
а max
Intensity:
Simple pendulum:
I= Pav
4ar?
T= 2n=
Doppler Shift:
Moving observer: f' = f(v+vo)/v
Speed sound temperature:
Moving source: f' = f(v)/ ( v-vs)
v= f2
Where vo = velocity of observer, vs is the
speed of the source, and v is the
speed of sound
T
U = (331m/s),
273K
Intensity of a wave:
power
Beat frequency fB
\f2- fil
I=
%3D
area
A
bol
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