Question

A cylinder of mass, M, radius, and moment of inertia I =
1/2Mρ^{2} rolls without

slipping at the bottom of a pipe of inside radius R.

a) What is the equation of constraint?

b) Find Lagrange’s equation of motion.

c) Find the frequency of small oscillations (use the approximation:
sin(θ) ≈ θ).

Answer #1

3) A solid cylinder with mass 4kg and radius r=0.5 m rolls
without slipping from a height of 10 meters on an inclined plane
with length 20 meters. a) Find the friction force so that it rolls
without slipping b) Calculate the minimum coefficient of rolling
friction mu c) Calculate its speed as it arrives at the bottom of
the inclined plane

A 1.6 m radius cylinder with a mass of 8.6 kg rolls without
slipping down a hill which is 5.6 meters high. At the bottom of the
hill, what percentage of its total kinetic energy is invested in
rotational kinetic energy?

A uniform cylinder of mass M and radius R rolls without slipping
down a slope of angle theeta to the horizontal. The cylinder is
connected to a spring constant K while the other end of the spring
is connected to a rigid support at P. The cylinder is released when
the spring is unstrectched. The maximum displacement of cylinder is
?

A hollow cylinder (hoop) of mass M and radius R starts rolling
without slipping (with negligible initial speed) from the top of an
inclined plane with angle theta. The cylinder is initially at a
height h from the bottom of the inclined plane. The coefficient of
friction is u. The moment of inertia of the hoop for the rolling
motion described is I= mR^2.
a) What is the magnitude of the net force and net torque acting
on the hoop?...

A thin cylinder starts from rest and rolls without slipping on
theloop-the loop with radius R. Find the minimum starting height of
the marblefrom which it will remain on the track through the loop.
Assume the cylinder radius is small compared to R.

A very thin circular hoop of mass m and radius
r rolls without slipping down a ramp inclined at an angle
θ with the horizontal, as shown in the figure.
What is the acceleration a of the center of the
hoop?

A cylinder of mass and radius R rolls without slipping down an
incline plane starting from ??rest at a height d above the ground.
The plane is angled 30 degrees from the horizontal. Ignoring air
resistance, find the speed and the
acceleration of the cylinder at the
bottom of the plane.
a.Use the methods of conservation of energy to solve
this problem.
b. Use the methods of torques to check your answer.
c. Look ? at your answer to this...

A uniform disc of mass M=2.0 kg and radius R=0.45 m rolls
without slipping down an inclined plane of length L=40 m and slope
of 30°. The disk starts from rest at the top of the incline. Find
the angular velocity at the bottom of the incline.

A sphere of mass M, radius r, and rotational inertia I is
released from rest at the top of an inclined plane of height h as
shown above. (diagram not shown)
If the plane has friction so that the sphere rolls without
slipping, what is the speed vcm of the center of mass at the bottom
of the incline?

A cylinder (radius = 0.14 m, center-of-mass rotational inertia =
0.015410 kg·m2, and mass = 1.49 kg) starts from rest and rolls
without slipping down a plane with an angle of inclination of
25.5°. Find the time it takes it to travel 1.62 m along the
incline.
NEED ANSWER ASAP

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