Question

An object (either solid sphere, hoop or solid disk) of Mass
**M=10kg** and radius **R=4m** is at the
bottom of an incline having **inclination angle X=40 degrees
and base length X=15 meters,** with an initial rotational
velocity **omega(i)=2rad/s;** it is subsequently
pulled up the the incline by some force **F=15**
**(Newtons)** such that at the top of the incline it
has a final rotational velocity **omega(f)=7rad/s**.
Determine: a) the linear velocity, b) rotational KE and c) total
work and work done by both the external force, as well as gravity
acting on the mass, once it's reached the top of the incline.

Now the mass is released from rest at the top; determine its final rotational velocity at the bottom of the incline, it's rotational KE, it's linear KE, as well as the work done by gravity as the mass rolls down. Remember that W(tot)=Delta(KE), including both rotational and also linear KE on the right-hand-side.

Answer #1

Problem 4
A hoop and a solid disk both with Mass (M=0.5 kg) and radius (R=
0.5 m) are placed at the top of an incline at height (h= 10.0 m).
The objects are released from rest and rolls down without
slipping.
a) The solid disk reaches to the bottom of the inclined plane
before the hoop. explain why?
b) Calculate the rotational inertia (moment of inertia) for the
hoop.
c) Calculate the rotational inertia (moment of inertia) for the...

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 solid, homogeneous sphere with of mass of M = 2.25 kg and a
radius of R = 11.3 cm is resting at the top of an incline as shown
in the figure. The height of the incline is h = 1.65 m, and the
angle of the incline is θ = 17.3°. The sphere is rolled over the
edge very slowly. Then it rolls down to the bottom of the incline
without slipping. What is the final speed of...

Consider the following three objects, each of the same mass and
radius:
1) Solid Sphere
2) Solid Disk
3) Hoop.
All three are release from rest at top of an inclined plane. The
three objects proceed down the incline undergoing rolling motion
without slipping. use work-kinetic energy theorem to determine
which object will reach the bottom of the incline first

1. A disk with a radius of 0.8 meters, a mass of 5 kg and c
value of 1/2 is rolling without slipping at down an incline with a
height (not length) of 6 meters. At the top of the incline, it is
spinning at 16 rad/s. How fast is it moving in m/s (center of mass
moving) at the bottom of the incline? Hint: first find how fast
it's moving at the top of the incline as was done...

A solid disk of mass m1 = 9.8 kg and radius R = 0.25 m is
rotating with a constant angular velocity of ω = 30 rad/s. A thin
rectangular rod with mass m2 = 3.9 kg and length L = 2R = 0.5 m
begins at rest above the disk and is dropped on the disk where it
begins to spin with the disk.
1)What is the initial angular momentum of the rod and disk
system?
2)What is the...

A solid disk of mass m1 = 9.3 kg and radius R = 0.21
m is rotating with a constant angular velocity of ω = 30 rad/s. A
thin rectangular rod with mass m2 = 3.8 kg and length L
= 2R = 0.42 m begins at rest above the disk and is dropped on the
disk where it begins to spin with the disk.
1)
What is the initial angular momentum of the rod and disk
system?
2)
What...

A solid disk of mass m1 = 9.5 kg and radius R = 0.19
m is rotating with a constant angular velocity of ω = 30 rad/s. A
thin rectangular rod with mass m2 = 3.3 kg and length L
= 2R = 0.38 m begins at rest above the disk and is dropped on the
disk where it begins to spin with the disk.
1) What is the initial angular momentum of the rod and disk
system?
2) What...

Suppose a solid sphere of mass 450 g and radius 5.00 cm rolls
without slipping down an inclined plane starting from rest. The
inclined plane is 7.00 m long and makes an angel of 20.0 o from the
horizontal. The linear velocity of the sphere at the bottom of the
incline is _______ m/s. please show work

A solid disk of mass m1 = 9.5 kg and radius R = 0.19
m is rotating with a constant angular velocity of ω = 30 rad/s. A
thin rectangular rod with mass m2 = 3.3 kg and length L
= 2R = 0.38 m begins at rest above the disk and is dropped on the
disk where it begins to spin with the disk.
5) What is the final rotational energy of the rod and disk
system?

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