# Rolling, Torque, and Angular Momentum

• ranjaxt2012
In summary, a girl of mass 28.1 kg throws a rock of mass 670 g horizontally from the rim of a frictionless merry-go-round with a radius of 1.58 m and rotational inertia of 433 kg·m2. The rock has a relative speed of 7.78 m/s to the ground. After the throw, the angular speed of the merry-go-round is approximately 0.81674 rad/s and the linear speed of the girl can be found using the equation v = ωr. The net angular and linear momentum of the system is conserved. The concept of velocity of the system is not applicable unless specified.
ranjaxt2012

## Homework Statement

A girl of mass 28.1 kg stands on the rim of a frictionless merry-go-round of radius 1.58 m and rotational inertia 433 kg·m2 that is not moving. She throws a rock of mass 670 g horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground, is 7.78 m/s. Afterward, what are (a) the angular speed of the merry-go-round and (b) the linear speed of the girl?

## Homework Equations

Mass M = 28.1 kg
R-Inertia = 433 Kg.m2
mass of rock = 670g = .67 kg (tangent to merry-go-round)
speed of rock = 7.78 m.s
now is the angular speed ω of merry-go-round = ?
we know ω = L/Inertia or (m.r.v)/inertia.
Now what is velocity of the system? is it 7.78?

## The Attempt at a Solution

if yes then

ω = [(28.1+.67)*1.58*7.78)]/433 ≈ 0.81674 rad/sec

is linear speed of the girl = 0.816748*r

v = ω/r ??

ranjaxt2012 said:

Now what is velocity of the system? is it 7.78?

## The Attempt at a Solution

if yes then

ω = [(28.1+.67)*1.58*7.78)]/433 ≈ 0.81674 rad/sec

is linear speed of the girl = 0.816748*r

v = ω/r ??

All you have to do is to conserve the net angular momentum of the system of rock , girl and merry go round as no net external torque acts on this system.
Infact the net linear momentum is also conserved as no net external force acts on this system. (just after throwing)

You said velocity of the system in your post.
You can't talk of the velocity of the system until you specify it.

if you mean the girl and merry go round, the NO

## 1. What is the difference between rolling, torque, and angular momentum?

Rolling is the movement of an object along a surface while also rotating around its own axis. Torque is the force that causes an object to rotate around an axis. Angular momentum is the measure of an object's tendency to continue rotating around an axis.

## 2. How do these concepts relate to each other?

Rolling and torque are directly related, as torque is what causes an object to roll. Angular momentum is also related to torque, as torque is the rate of change of angular momentum.

## 3. What is the formula for calculating torque?

Torque is equal to the force applied to an object multiplied by the distance from the point of rotation at which the force is applied. The formula is T = F x d, where T is torque, F is force, and d is distance.

## 4. How does the distribution of mass affect rolling, torque, and angular momentum?

The distribution of mass affects an object's moment of inertia, which is a measure of how difficult it is to change an object's rotational motion. Objects with more mass distributed farther from the axis of rotation will have a larger moment of inertia, making it more difficult to change their rotation. This affects the amount of torque and angular momentum an object will have.

## 5. Can rolling, torque, and angular momentum be applied to non-circular objects?

Yes, these concepts can be applied to any object that rotates around an axis. Non-circular objects may have a more complex path of rolling, and torque and angular momentum calculations may require more advanced mathematical methods, but the principles still apply.

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