# Rotation and Linear Motion Help

• choi626
In summary, according to the student, the masses are connected because they need to conserve momentum and the smaller mass is inside the larger one.
choi626

## Homework Statement

Two masses, m1 and m2, are connected by light cables to the perimeters of two cylinders of radii, r1 and r2, respectively. The cylinders are rigidly connected to each other but are free to rotate without friction on a common axle. The moment of inertia of the pair of cylinders is I = 45 kgm^2.
r1= 0.5m
r2= 1.5m
m1= 20kg
a) Find the mass of m2 so that the system is in equilibrium
b) the mass is removed and the system released from rest. Determine the angular acceleration, the cable supporting m1, and the linear speed of m1 at the time it has descended 1m.

## The Attempt at a Solution

a) T=0
r1F1 - r2F2 = 0
m2= 6.7kg.

b)T=I(alpha)
then how do i go on?

What do you visualize happening to the mass and cylinders after the balancing mass is removed?

the wheel rotating in the direction of the heavier mass.

okay umm so my teacher wrote that i have to connect the bodies as well. do i combine the inertias of the two masses

I = I(of m1) + I(of m2).

but he marked it wrong saying i need to connect the bodies. I don't think i fully understand what he means.

w/o a pic, not sure either. I was under the impression that the cylinders were held stationary while the balancing mass was removed and then allowed to accelerate. In other words you had one mass, two cylinders and a brake which was released at t=0

Re

yea so i was kinda pissed he didnt put a pic on the test too. but he said that the cylinders are instantaneously stationary when the mass is removed. The smaller cylinder he said can be considered to be inside the big one. The only reason for the two radii is for the inertia equations for the masses.

ok, then the reason they are "connected" is thru the need to conserve momentum. I'm headed for zzzzland, suspect there will be more on this issue in the morning.

## 1. What is the difference between rotation and linear motion?

Rotation is the movement of an object around an axis or center point, while linear motion is the movement of an object in a straight line.

## 2. How is rotational motion measured?

Rotational motion is measured in units of angle, such as degrees or radians. The amount of rotation can be determined by calculating the change in angle from the starting position.

## 3. What is the relationship between angular velocity and linear velocity?

Angular velocity is the rate at which an object rotates around an axis, while linear velocity is the rate at which an object moves in a straight line. The two are related by the formula v = rω, where v is linear velocity, r is the radius of rotation, and ω is angular velocity.

## 4. How does rotational inertia affect an object's motion?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. Objects with a larger rotational inertia will require more force to rotate and will rotate more slowly compared to objects with a smaller rotational inertia.

## 5. Can rotational motion be converted to linear motion?

Yes, rotational motion can be converted to linear motion through the use of gears, pulleys, or wheels. These mechanisms allow the rotational motion of one object to be translated into linear motion of another object.

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