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## PowerPoint Slideshow about ' Lecture 14 – Rigid Body Kinematics' - tyson

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Particle vs. rigid body mechanics

- What is the difference between particle and rigid body mechanics?
- Rigid body – can be of any shape
- Block
- Disc/wheel
- Bar/member
- Etc.
- Still planar
- All particles of the rigid body

move along paths equidistant

from a fixed plane

- Can determine motion of

any single particle (pt)

in the body

particle

Rigid-body (continuum of particles)

Types of rigid body motion

- Kinematically

speaking…

- Translation
- Orientation of AB

constant

- Rotation
- All particles rotate

about fixed axis

- General Plane Motion

(both)

- Combination of both

types of motion

B

B

B

B

A

A

A

A

Kinematics of translation

- Kinematics
- Position
- Velocity
- Acceleration
- True for all points in R.B. (follows particle kinematics)

y

rB

rA

x

B

A

Simplified case of our relative motion of particles discussion – this situation same as cars driving side-by-side at same speed example

fixed in the body

Rotation about a fixed axis – Angular Motion

r

- In this slide we discuss the motion of a line or body since these have dimension, only they and not points can undergo angular motion
- Angular motion
- Angular position, θ
- Angular displacement, dθ
- Angular velocity

ω=dθ/dt

- Angular Acceleration
- α=dω/dt

Counterclockwise is positive!

Angular velocity

angular velocity vector always perpindicular to plane of rotation!

http://www.dummies.com/how-to/content/how-to-determine-the-direction-of-angular-velocity.html

Magnitude of ω vector = angular speed

Direction of ω vector 1) axis of rotation

2) clockwise or counterclockwise rotation

How can we relate ω & αto motion of a point on the body?

Relating angular and linear velocity

- v = ωx r, which is the cross product
- However, we don’t really need it because θ = 90° between our ω and r vectors we determine direction intuitively
- So, just use v = (ω)(r) multiply magnitudes

http://www.thunderbolts.info

http://lancet.mit.edu/motors/angvel.gif

Rotation about a fixed axis – Angular Motion

r

- In this slide we discuss the motion of a line or body since these have dimension, only they and not points can undergo angular motion
- Angular motion
- Angular position, θ
- Angular displacement, dθ
- Angular velocity

ω=dθ/dt

- Angular Acceleration
- α=dω/dt
- Angular motion kinematics
- Can handle the same way as rectilinear kinematics!

Axis of rotation

In solving problems, once know ω & α, we can get velocity and acceleration of any point on body!!!

(Or can relate the two types of motion if ω & α unknown )

Example problem 1

When the gear rotates 20 revolutions, it achieves an angular velocity of ω = 30 rad/s, starting from rest. Determine its constant angular acceleration and the time required.

Example problem 2

The disk is originally rotating at ω0 = 8 rad/s. If it is subjected to a constant angular acceleration of α = 6 rad/s2, determine the magnitudes of the velocity and the n and t components of acceleration of point A at the instant t = 0.5 s.

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