# 7-Rotational Motion

## Resources

**Slideshows**:Rotational Kinematics notes, Rotational Dynamics (Torque, Inertia and acceleration), and Rotational Energy and Momentum Notes

**Textbook**: Chapters 7 & 8 in Mastering Physics (get online code for registration on about page of google classroom)

**External Resources**

http://www.rpi.edu/dept/phys/Dept2/APPhys1/torque/torque/node6.html a site with some basic torque practice and explanations.

## Objectives

Describe rotational motion

use angular displacement, angular velocity and angular acceleration to describe motion about a fixed axis

relate rotational motion to linear motion using the radius

use + or or - for counterclockwise or clockwise motion.

Torque Basics

Use representations of the relationship between force and torque.

Compare torques on an object caused by forces

Estimate torque on an object

In equilibrium

Design an experiment & analyze data testing a question about balanced torques in a rigid body system

Calculate torques in 2D while in static equilibrium (from a diagram or model)

Center of mass

analyze the motion of a system of 2 objects based on their center of mass

in the case of rotation, a force going through the center of mass causes no torque.

Unbalanced torques

Net torque causes acceleration

calculate angular acceleration from the net torque and rotational inertia of an object or rigid system

predict angular velocity changes when forces cause a net torque on an object rotating on a fixed axis.

Net Torque causes a change in momentum

Angular Momentum

basics

Use right hand rule to find direction of angular momentum (classify as + or -)

relate angular momentum to linear momentum by using the radius

relate angular momentum to rotational inertia and angular velocity

Consider the locations and velocities of individual parts of a system to describe & calculate the angular momentum of a system

In particular, calculate momentum for a system of a point mass and extended object

changing momentum

relate change in angular momentum to average torque and the amount of time the torque is applied.

zero net torque indicates momentum is conserved

changes in mass distribution can affect the angular speed of a system without changing momentum

Consider elliptical orbits in earth-satellite system

collisions can cause exchanges of angular momentum

predict the effects of a collision in terms of rotational behaviors by finding total momentum before and after a collision.

multiple objects rotating together can be treated as a single system with a combined momentum

find the change of angular momentum in unfamiliar circumstances & plan labs

## Equations

In addition to the equations above (on the formula chart), you should memorize or be able to recreate the following:

use r to convert between angular and linear quantities (v = ωr, a = ⍺r, d=𝜃r)

Replace angular quantities in linear equations -- like v

^{2}= v_{0}^{2}+ 2a(x-x_{0}).Create simple definitions for average angular quantities, like average angular acceleration = change in angular velocity divided by time, as we did with linear quantities

Know that I = mr

^{2}for point objects at the edge of a circle or hoops, I = 1/2 mr^{2}for disks or cylinders, and is even less (2/5mr^{2}) for spheres.Show that the angular momentum of a linearly traveling object can be found by L=mvr (or in other words, L=pr)

## Viral Physics videos

This is an amazing build project that actually uses what we talk about with torque, rotational energy, rotational inertia, and some really cool variations to create a near perfect transfer of energy.

This dude has come insane core strength to hold this pose. How would you analyze the forces/torques in this equilibrium situation?

## Common Misconceptions

**Misconception:**Any force acting on an object will produce a torque.**Principle:**Force components perpendicular to the radius (or forces with moment arms) cause torque**Reasoning:**Torque is a measurement of a tendency to change rotation and in order to do that a force must in a way where the line of action of the force does not pass through the center of mass of a free moving object or the pivot point of a fixed object. If it does pass through these points it will affect the whole object equally and not cause rotation, where if it acts to one side or other of the pivot or center, it will cause that side to move along with the force while the other side pivots around the other way.

**Misconception:**Objects moving in a straight line can not have angular momentum.**Principle**: If an object can give angular momentum to a second object, it must have angular momentum to begin with.**Reasoning:**Many systems/objects can be evaluated multiple ways. Straight line motion, if considered from a point of rotation that matters for the system, can can be described in terms of how many radians/s it moves as opposed to m/s. While the angular velocity will be increasing as it gets closer to the pivot, the r value will be decreasing and as a result the overall angular momentum of the object a remains constant L=mvr (as shown in the diagram where p=mv and D is the shortest R of the path. This is only meaningful if the angular momentum is going to be transferred to a second object; otherwise it is not intuitive.

**Misconception:**Torque is the same as force and is in same direction.**Principle:**Torque is a tendency to rotate caused by force with a direction that is 90 degrees to the force and moment arm as determined by the right hand rule.**Reasoning:**The direction of torque is not terribly important until you talk about changing angular momentum, in which case we see weird stuff like gyroscopic precession (google it and be amazed). This behavior is explained most directly by assigning the direction for angular momentum and torque according to the right hand rule.

**Misconception:**The direction of angular momentum is in direction of linear momentum.**Principle:**The direction of angular momentum is determined by the right hand rule.**Reasoning:**Use the same diagram as above for either angular speed or angular momentum, but alter it by using your fingers to represent the movement ov the rotating object, as opposed to the force acting on it. It will always be a direction that is 90 degrees to the plane of rotation, which is weird, but required for things like gyroscopic precession to make sense.