Question

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.

Answer #1

Let us assume the cylinder was released from a height of h and let it has a velocity v at the top of the loop.

By the law of conservation of energy

The moment of inertia of the thin cylinder is given by

That gives us

In this rotational motion without slipping

that gives us

To stay on the top

Putting this value

**That gives us the initial height**

A solid 0.5750-kg ball rolls without slipping down a track
toward a loop-the-loop of radius R = 0.6550 m. What minimum
translational speed vmin must the ball have when it is a height H =
1.026 m above the bottom of the loop, in order to complete the loop
without falling off the track?

A solid 0.595-kg ball rolls without slipping down a track toward
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speed vmin must the ball have when it is a height H = 1.091 m above
the bottom of the loop, in order to complete the loop without
falling off the track?

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 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 cylinder rolls without slipping down an incline starting
from rest. At the same time a box starts from rest at the same
altitude and slides down the same incline with negligible friction.
Which arrives at the bottom first?
A. It is impossible to determine.
B. the box
C. the cylinder
D. Both arrive at the same time.

A basketball starts from rest and rolls without slipping down a
hill. The radius of the basketball is 0.23 m, and its 0.625 kg mass
is evenly distributed in its thin shell. The hill is 50 m long and
makes an angle of 25° with the horizontal. How fast is it going at
the bottom of the hill?
Group of answer choices
10.7 m/s
12.3 m/s
15.8 m/s
14.4 m/s
17.2 m/s

A basketball starts from rest and rolls without slipping down a
hill. The radius of the basketball is 0.23 m, and its 0.625 kg mass
is evenly distributed in its thin shell. The hill is 50 m long and
makes an angle of 25° with the horizontal. How fast is it going at
the bottom of the hill?
Group of answer choices
17.2 m/s
14.4 m/s
10.7 m/s
12.3 m/s
15.8 m/s

A sphere of radius r=34.5 cm and mass m= 1.80kg starts from rest
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