Question

An green hoop with mass
m_{h} = 2.7 kg and radius R_{h} = 0.15 m
hangs from a string that goes over a blue solid disk pulley with mass
m_{d} = 2.1 kg and radius R_{d} = 0.09 m.
The other end of the string is attached to a massless axel through
the center of an orange sphere on a flat horizontal surface that
rolls without slipping and has mass m_{s} = 3.7 kg and
radius R_{s} = 0.19 m. The system is released from
rest.

1. What is magnitude of the linear acceleration of the sphere?

2. What is the magnitude of the angular acceleration of the disk pulley?

3. What is the magnitude of the angular acceleration of the sphere?

4. What is the tension in the string between the sphere and disk pulley?

Answer #1

A green hoop with mass mh = 2.4 kg and radius Rh = 0.14 m hangs
from a string that goes over a blue solid disk pulley with mass md
= 2.3 kg and radius Rd = 0.08 m. The other end of the string is
attached to an orange block on a flat horizontal surface that
slides without friction and has mass m = 3.6 kg (see Figure 1). The
system is released from rest.
(a) What is magnitude...

A circular hoop (?hoop ?? ) of mass ? 5.00 kg, radius ? 2.00 m,
and infinitesimal thickness rolls without slipping down a ramp
inclined at an angle ? 32.0° with the horizontal.
(a) Draw a free body diagram of the hoop. [1]
(b) Determine the magnitude of the hoop’s acceleration down the
ramp. [4]
(c) Determine the force of static friction on the hoop. [3]

A
1.53kg bucket hangs on a rope wrapped around a pulley of mass
7.07kg and radius 66cm. This pulley is frictionless in its axle,
and has the shape of a solid uniform disk.
A. Explain conceptually why the moment of inertia of
this pulley is less than the moment of inertia of a hoop around its
center with the same mass and circumference as the
pulley.
B. What is the angular acceleration of the
pulley?
C. What is the acceleration...

A hoop and a disk, both of 0.88- m radius and 4.0- kg mass, are
released from the top of an inclined plane 3.3 m high and 8.1 m
long. What is the speed of each when it reaches the bottom? Assume
that they both roll without slipping. What is the speed of the
hoop? What is the speed of the disk?

A hoop and a disk, both of 0.50- m radius and 4.0- kg mass, are
released from the top of an inclined plane 2.9 m high and 8.7 m
long. What is the speed of each when it reaches the bottom? Assume
that they both roll without slipping. What is the speed of the
hoop? What is the speed of the disk?

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?

The pulley is a uniform cylinder with mass m3 = 0.400 kg and
radius R= 4.00 cm, the other two masses are m1 = 2.00 kg and m2 =
1.00 kg, and α = 35.0 degrees. Assume the rope is massless, there
is no slipping of the rope on the pulley, there is no friction
between m1 and the incline, and the incline position is fixed.
(a)
What is the acceleration of m1 and m2 (both magnitude and
direction)? What...

A disk with mass m = 6.3 kg and radius R = 0.46 m hangs from a
rope attached to the ceiling. The disk spins on its axis at a
distance r = 1.53 m from the rope and at a frequency f = 19.7 rev/s
(with a direction shown by the arrow).
1)
What is the magnitude of the angular momentum of the spinning
disk?
kg-m2/s
2)
What is the torque due to gravity on the disk?
N-m
3)...

A counterweight of mass m = 4.30 kg is attached to a light cord
that is wound around a pulley as shown in the figure below. The
pulley is a thin hoop of radius R = 7.00 cm and mass M = 1.60 kg.
The spokes have negligible mass. (a) What is the net torque on the
system about the axle of the pulley? magnitude N · m direction (b)
When the counterweight has a speed v, the pulley has...

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...

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