Question

In experiment 1 ( Moment of inertia), when changing the mass of the weight and the radius of the step pulley, how does the magnitude of the moment of inertia change?

Answer #1

Moment of inertia of a body is the torque required to give it angular acceleration. It is analogous to the mass in linear motion, as for mass we need force to give it linear accleration.

For a body moment of inertia depends upon the mass distribution
of the body and their distance from the axis of rotation.,
where I is Moment Of Inertia. For a point body it is given by I =
mr^{2}.

So, changing the mass of the body ( mass distribution) or radius of the body (also mass distribution change) will change the moment of inertia according to above formula.

During the Moment of Inertia experiment, group of students
decided to mount solid cylinder on the top of the horizontal disk.
The cylinder and disk have the same mass, M, and radius, R. The
friction was removed from the system. The falling mass, Ill, was
1/9 of the mass of the disk and the radius of the solid cylinder is
10 times greater than radius of the pulley.
(a) Calculate the moment of inertia of the disk and solid
cylinder...

Answer the following questions about moment of inertia:
1) What is the physical significance of the y-intercept (I0)?
(MOMENT OF INERTIA (I) VS RADIUS (r^2) graph)
2) How might the friction influence the calculations of moment
of inertia?
3) When a figure skater does a spin and then pulls in his/her
arms, the spin rate increases. Why is this?

Explain why when deriving the formula for the moment of inertia
for a body mass, one must consider the surface mass density when
defining one's differential mass element?

Find the moment of inertia of a uniform hollow sphere of mass M,
inner radius r, and outer radius R > r, about an axis through
the center of mass. Consider your answer for the cases r → 0 and r
→ R. Does the result reduce correctly? Explain.

(a) Find the moment of inertia, I, for a rod of length L and
mass M for an arbitrary axis that is at distance of x from its one
edge. (b) Now find the moment of inertia when the axis is at one
edge. (c) Find the moment of inertia when the axis is in the
middle.
Please leave detailed steps

1. Find the moment of inertia of a stick of length 4 m and mass
10 kg that is rotated about an axis that is 30 % from the left end
of the stick. Hint do the integration of r^2 dm
2. A 123 kg merry go round with a 5 m radius rotates on a
vertical axis. If I push at the edge with a force of 188 N, find
the angular acceleration. The moment of inertia of disk...

In
the experiment of moment of inertia, are there any torques being
ignored? What are they? Do they may significantly altered the
results?

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...

ball of mass m1
=5.9
kg and a block of mass m2
=3.3
kg are connected with a lightweight string over a pulley with
moment of inertia I and radius R=0.25m. The coefficient of kinetic
friction between the table top and the block of mass
m2
is
μk
= 0.5.
If the magnitude of the acceleration is a=2.9m/s2.
a)What are the tensions T1
and T2
in the string.
T1=
N
T2=
N
b)Calculate the moment of inertia of the pulley....

A green drum with a moment of inertia of 19.24kgm^2 and radius
0.95m rotates freely about a vertical axis. A rope is wound around
it and strung over a red wheel with a moment of inertia of
16.11kgm2 and radius 0.71m that rotates freely about a horizontal
axis. The rope is then attached to a cube dangling below with a
mass of 13.47kg. The cube falls 1.8m1.8m from rest. Take the
acceleration of gravity to be 9.81ms^2. Assume that the...

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