Question

A motor applies a torque of M = 50 Nm to a pulley in order to raise a 6 kg crate. The pulley has a mass of 20 kg and has a radius of gyration of ko = 0.8 m. The inner radius of the pulley (about which the cord is wrapped) is 0.75 m. How long would it take for the crate to reach a velocity of 5 m/s starting from rest?

Answer #1

To start her lawn mower, Julie pulls on a cord that is wrapped
around a pulley. The pulley has a moment of inertia about its
central axis of III = 0.590 kg⋅m2kg⋅m2 and a radius of 4.00 cmcm .
There is an equivalent frictional torque impeding her pull of
τfτftau_f = 0.260 m⋅Nm⋅N .
To accelerate the pulley at ααalpha = 4.35 rad/s2rad/s2 , how
much torque does Julie need to apply to the pulley?
How much tension must the...

a. Through how many revolutions does a frisbee
have to rotate to reach an angular speed of 570 rad/s if it starts
from rest and experiences a constant angular acceleration of 160
rad/s2?
b. How long does it take the frisbee to reach the angular speed
of 570 rad/s?
c. A cord is wrapped around a pulley of radius 33.0 cm and mass
4.00 kg. A tension of 15.0 N is applied to end of the cord. A
friction torque...

Problem 2. (based on Young & Freedman 9.47) A frictionless
pulley has the shape of a uniform solid disk of mass 2.50 kg and
radius .0200 m. A stone of unknown mass is attached to a very light
wire that is wrapped around the rim of the pulley. When the system
is released from rest, the stone accelerates downward at 5.9 m/s 2
(a) What is the angular acceleration of the pulley? Answer: 295
rad/s 2 (b) Find the torque...

The drive chain in a bicycle applies a torque of 0.850 N∙m to
the wheel of the bicycle. The wheel has a mass of 0.750 kg and can
be assumed to all be located on the rim, at a radius of 0.330 m.
What is the angular acceleration of the wheel?

I want only final answer
8. A flywheel has a mass of 100 kg and a radius of gyration kG =
100 mm about an axis of rotation passing through its mass center.
If a motor supplies a clockwise torque having a magnitude of M= 9 t
Nm, where t is in seconds, determine the flywheel’s angular
velocity in t = 5s. Initially the flywheel is rotating clockwise at
ω1 = 4 rad/s

A frictionless pulley has the shape of a uniform solid cylinder
of mass 2.5 kg and radius 15 cm. A 2.1 kg stone is attached to a
very light wire that is wrapped around the rim of the pulley, and
the system is released from rest. When the stone has lost 3J of
gravitational potential energy, how much kinetic energy does the
pulley have?
The Answer is 1.1 J I just don't know how to reach this
answer.

A motor spins a disk (Idisk = 24.2 kg*m2) with a torque of 39
N*m, and a 18 N frictional force acts on the disk at a radius of
1.3 m. Attached to the disk at a radius of 1.8 m is a 10 kg mass.
What is the magnitude of the angular acceleration in rad/s2 of the
system?

A string passing over a pulley has a 3.75-kg mass hanging from
one end and a 2.75-kg mass hanging from the other end. The pulley
is a uniform solid cylinder of radius 4.9 cmcm and mass 0.80
kg.
A) If the bearings of the pulley were frictionless, what would
be the acceleration of the two masses?
B) In fact, it is found that if the heavier mass is given a
downward speed of 0.25 m/s , it comes to rest...

The pulley shown below has a mass of 3.00 kg and radius R = 60.0
cm, and can be treated as a uniform solid disk that can rotate
about its center. The block (which has a mass of m = 900 g) hanging
from the string wrapped around the pulley is then released from
rest. Use g = 10 m/s2. When the block has dropped through a
distance of 2.00 m, what is the block's speed?

A hanging weight, with a mass of m1 = 0.365
kg, is attached by a cord to a block with mass
m2 = 0.815 kg as shown in the figure below. The
cord goes over a pulley with a mass of M = 0.350 kg. The
pulley can be modeled as a hollow cylinder with an inner radius of
R1 = 0.0200 m, and an outer radius of
R2 = 0.0300 m; the mass of the spokes is
negligible. As...

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