Question

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

Answer #1

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?...

1. A solid sphere of mass 50 kg rolls without slipping. If the
center-of-mass of the sphere has a translational speed of 4.0 m/s,
the total kinetic energy of the sphere is
2.
A solid sphere (I = 0.4MR2) of
radius 0.0600 m and mass 0.500 kg rolls without slipping down an
inclined plane of height 1.60 m . At the bottom of the plane, the
linear velocity of the center of mass of the sphere is
approximately
_______ m/s.

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 solid, uniform sphere of mass 2.0 kg and radius 1.7m rolls
without slipping down an inclined plane of height 7.0m . What is
the angular velocity of the sphere at the bottom of the inclined
plane? a) 5.8 rad/s b) 11.0 rad/s c) 7.0 rad/s d) 9.9 rad/s

A solid cylinder starts rolling without slipping from the top of
an inclined plane. The cylinder starts moving from rest at a
vertical height 10m. The mass of the cylinder is 1kg and its radius
is .5m. The moment of inertia of the cylinder is 1/2 mr2
(where m is the mass of the cylinder and r is its radius).
C.What is the rotational kinetic energy of the cylinder when its
vertical height is 3 m?
D.What is the translational...

A solid cylinder starts rolling without slipping from
the top of an inclined plane. The cylinder starts moving from rest
at a vertical height 10m. The mass of the cylinder is 1kg and its
radius is .5m. The moment of inertia of the cylinder is 1/2
mr2 (where m is the mass of the cylinder and r is its
radius).
What is the speed of the center of mass of the
cylinder when its vertical height is 4 mm ?...

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 solid cylinder starts rolling without slipping from the top of
an inclined plane. The cylinder starts moving from rest at a
vertical height 10m. The mass of the cylinder is 1kg and its radius
is .5m. The moment of inertia of the cylinder is 1/2 mr2
(where m is the mass of the cylinder and r is its radius).
1.What is the speed of the center of mass of the cylinder when
its vertical height is 5 mm ?...

Rotation (rolling without slipping)
Two cylinders with a radius r=0.650 m are rolled without slipping
down an incline that descends a vertical distance of 2.45 meters.
Each cylinder has equal mass m=3/68 kg, but one is solid and the
other is a hollow shell.
A) What is the center of mass velocity of the solid cylinder at the
bottom of the incline?
B) What is the center of mass velocity of the hollow cylinder 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?

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