Question
In: Physics
The angle through which a rotating wheel has turned in time t is given by θ...
The angle through which a rotating wheel has turned in time t is given by θ = a t− b t2+ c t4, where θ is in radians and t in seconds
PART A
If a = 9.0 rad/s , b = 15.5 rad/s2 , c = 1.6 rad/s4 , evaluate ω at t = 3.2 s .
Express your answer using two significant figures
PART B
Evaluate α at t = 3.2 s .
Express your answer using two significant figures.
PART C
What is the average angular velocity between t = 2.0 s and t =3.2 s ?
Express your answer using two significant figures
PART D
What is the average angular acceleration between t = 2.0 s and t =3.2 s ?
Express your answer using two significant figures.
Solutions
genius_generous answered 8 months agoRelated Solutions
3. The angle that a wheel rotates as a function of time "t" is given by...
3. The angle that a wheel rotates as a function of
time "t" is given by θ (t) = 8.5–15.0t ^ 2 + 1.6t ^ 4 where θ is in
radians and "t" in seconds. (a) Determine an expression for the
instantaneous angular velocity ω. (b) Determine an expression for
the instantaneous angular acceleration α. (c) Evaluate ω and α at t
= 3.0s. (d) What is the average angular velocity at t = 2.0s and t
= 3.0s? (e)...
The angular position of a point on the rim of a rotating wheel is given by...
The angular position of a point on the rim of a rotating wheel
is given by θ = 9.33t - 3.93t2 + 1.09t3, where θ is in radians and
t is in seconds. What are the angular velocities at (a) t = 2.13 s
and (b) t = 8.41 s? (c) What is the average angular acceleration
for the time interval that begins at t = 2.13 s and ends at t =
8.41 s? What are the instantaneous angular...
A potter's wheel is rotating around a vertical axis through its center at a frequency of...
A potter's wheel is rotating around a vertical axis through its
center at a frequency of 1.7 rev/s. The wheel can be considered a
uniform disk of mass 5.0 kg and a diameter of 0.32 m. The potter
then throws a 2.8-kg chunk of clay, approximately shaped as a flat
disk of radius 8.0 cm, onto the center of the rotating wheel.
What is the frequency of the wheel after the clay sticks to it?
Ignore friction.
A potter's wheel is rotating around a vertical axis through its center at a frequency of...
A potter's wheel is rotating around a vertical axis through its
center at a frequency of 1.6 rev/s . The wheel can be considered a
uniform disk of mass 6.0 kg and diameter 0.50 m . The potter then
throws a 2.2-kg chunk of clay, approximately shaped as a flat disk
of radius 7.1 cm , onto the center of the rotating wheel.
Part A
What is the frequency of the wheel after the clay sticks to
it?
Suppose θ is an acute angle in a right triangle. Given tan(θ)=1/5, evaluate: 1-sin^2(θ)
Suppose θ is an acute angle in a right triangle. Given
tan(θ)=1/5, evaluate: 1-sin^2(θ)
During 0.24 s, a wheel rotates through an angle of 2.42 rad as a point on...
During 0.24 s, a wheel rotates through an angle of 2.42 rad as a
point on the periphery of the wheel moves with a constant speed of
2.48 m/s. What is the radius of the wheel?
A rotating wheel obeys the equation theta(t)= 8.9t-14.0t^2+1.84t^4 where theta is in radians and t is...
A rotating wheel obeys the equation theta(t)=
8.9t-14.0t^2+1.84t^4 where theta is in radians and t is in
seconds.
What is ω at t = 4.0 s? Use 'rad/s' for your units.
What is α at t = 4.0 s? Use 'rad/s^2' for your units.
What is the average angular velocity between t = 1.0 s and 2.0
s? Use 'rad/s' for your units.
What is the average angular acceleration between t = 1.0 s and
2.0 s? Use 'rad/s^2' for...
A rotating wheel requires 2.97-s to rotate through 37.0 revolutions. Its angular speed at the end...
A rotating wheel requires 2.97-s to rotate through 37.0
revolutions. Its angular speed at the end of the 2.97-s interval is
97.0 rad/s. What is the constant angular acceleration of the wheel?
_____ rad/s2
Consider the sine-Gordon equation (SGE) θxt =sinθ, (1) which governs a function θ(x,t). For any given...
Consider the sine-Gordon equation (SGE)
θxt =sinθ, (1)
which governs a function θ(x,t). For any given λ denote the
following B ̈acklund trans- formation by BTλ:
1
θ −θx=2λsin 2(θ +θ) , (2a)
2 1
θ +θt=λsin 2(θ −θ) , (2b)
(a) Given a solution θ(x, t) of the SGE, show that θ(x, t) also
satisfies the SGE. Hint: Try calculating the t derivative of
Equation (2a) and the x-derivative of Equation (2b) and then taking
a sum or difference.
Find T(t), N(t), aT, and aN at the given time t for the space curve r(t)....
Find T(t), N(t), aT, and aN at the given time t for the space
curve r(t). [Hint: Find a(t), T(t), aT, and aN. Solve for N in the
equation a(t)=aTT+aNN. (If an answer is undefined, enter
UNDEFINED.)
Function Time
r(t)=9ti-tj+(t^2)k t=-1
T(-1)=
N(-1)=
aT=
aN=
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