# Solving Inertia Problems: 6 Questions Answered

• dnt
In summary, this conversation covers various problems involving rotational dynamics, including calculating forces, angular acceleration, angular speed, and moments of inertia. The first problem involves a large roll of paper held in place by a bracket attached to a rod, and a vertical force being applied to unroll the paper. The second problem involves a bullet striking a wooden board in a shooting gallery and finding the resulting angular speed and maximum height. The third problem discusses the collapse of a star into a neutron star and finding the angular speed of the neutron star. The fourth problem involves a child running out on a rotating turntable and finding the resulting angular speed. The fifth problem deals with a door being struck by mud and finding the final angular speed. The final problem involves a

## Homework Statement

1) A large 14 kg roll of a paper (radius = 19 cm) rests against the wall and is held in place by a bracket attached to a rod through the center of the roll. the rod turns without friction in the bracket and the moment of inertia of the paper and the rod about the axis is .240 kgm2. the other end of the bracket is attached by a frictionless hinge to the wall such that the bracket makes an angle of 30 degrees with the wall. (weight of bracket is negligible). the coefficient of kinetic friction between the paper and wall is .25. a constant vertical force of 40 N is applied to the paper and it unrolls.
--> What is the force that the rod exerts on the paper as it unrolls?
--> What is the angular acceleration of the roll?

2) a target in a shooting gallery consists of a vertical square wooden board (.25 m on each side, mass = .75 kg) that pivotes on the axis along its top edge. the board is struck face on at its center by a bullet with mass 2 g that is traveling at 350 m/s and is embedded into the board.
--> What is the angular speed of the board after the bullets impact?
--> What max height above equilibrium does the center of the board reach before starting to swing down again?
--> What minimum bullet speed would be required for the board to swing all the over after impact?

3) Under some circumstances a star can collapse into an extremely dense object made mostly of neutrons - the density of a neutron star is about 10^14 times greater than ordinary solid matter. suppose we represent the star as a great uniform, solid, rigid sphere both before and after collapse. the stars initial radius was 8 x 10^5 km and its final radius is 16 km. if the original star rotated once in 25 days, find the angular speed (in rad/s) of the neutron star.

4) A large turntable rotates about a fixed vertical axis, making one revolution in 5 sec - the moment of inertia of the turntable about this axis is 1400 kgm2. a child of mass 31 kg, initially standing at the center of the turntable, runs out along a radius. what is the angular speed (in rad/s) of the turntable when the child is 3 m from the center (assume you can treat the child as a particle).

5) A solid wood door 1 m wide and 2 m high is hinged along one side and has a mass of 53 kg. initially open and at rest, the door is struck at its center by a handful of sticky mud with mass .5 kg, traveling perpendicular to the door at 14 m/s just before impact. find the final angular speed of the door.

6) An experimental bicycle wheel is placed on a test stand so that it is free to turn on its axle. if a constant net torque of 7 Nm is applied to the tire for 2 sec, the angular speed increases from 0 to 100 rev/min. the external torque is then removed and the wheel is brought to rest by friction in its bearings in 110 seconds.

--> Compute the moment of inertia of the wheel about the rotation axis
--> Compute the friction torque
--> Compute the total number of revolutions made by the wheel in the 110 seconds.

dont know

## The Attempt at a Solution

honestly, i just do NOT get inertia. if someone could help me out id very much appreciate it. don't have to give me answers, but give me somewhere to start - how to set up equations/what each variable represents/what should i be looking at/what thigs mean/etc. usually in physics i get the concepts somewhat but inertia just doesn't click with me. just don't get it

i really want to learn too. but right now I am just having trouble with this topic. thanks for any help.

honestly, i just do NOT get inertia

Pick up something reasonably heavy and hold it with your arm held straight out in front of you. Now move your arm horizontally to and fro. Do you feel the resistance to the motion ? That's inertia. The downward pull is the weight.

Basically, if you have a mass on a stick and you try to rotate it at one end, the work you have to do to get it rotating depends on the 'moment of inertia'. The longer the stick the greater the moment. Also the massier the mass, the greater is the moment.

All you need is Newton's laws and the equations for the rotational equivalents.

You can find these in any basic textbook on mechanics, or your course notes.

so do you just set the equations equal to each other (kind of like setting PE = KE in an energy question)? conservation of inertia?

Draw a diagram of the problem setup, and mark the forces as arrows. Then apply what you know of dynamics. No one here is going to do the problems for you.

Maybe you should do some easier problems first, like how long does it take for something to fall 1m after being released ?

## 1. What is inertia and why is it important to solve inertia problems?

Inertia is the tendency of an object to resist changes in its state of motion. It is important to solve inertia problems because understanding and controlling inertia can help us design more efficient machines and vehicles, as well as prevent accidents.

## 2. How do you calculate inertia?

Inertia is calculated by multiplying an object's mass by the square of its velocity. The formula for inertia is I = m * v^2, where I is inertia, m is mass, and v is velocity.

## 3. What are some common examples of inertia problems?

Examples of inertia problems include a car skidding on an icy road, a rocket launching into space, and a person falling off a moving skateboard.

## 4. How can you solve inertia problems?

Inertia problems can be solved by understanding the principles of inertia and applying them to the specific situation. This may involve adjusting the mass or velocity of an object, using external forces to counteract inertia, or changing the direction of motion.

## 5. How can solving inertia problems benefit society?

By solving inertia problems, we can improve the efficiency and safety of transportation and machinery, leading to reduced energy consumption and fewer accidents. In addition, a better understanding of inertia can also aid in the development of new technologies and advancements in various fields of science and engineering.