Test 2 Material

Axis of Rotation

- A fixed line about which a body rotates - Will always be perpendicular to its plane

Rigid Body

A body that maintains a constant shape Example: A baseball bat

Displacement

A change in position

Position

A distance from the origin

Center of Mass (COM)

A fictitious point where all mass is considered to be connected

Linear velocity (v)

A point on a rotating body is determined by: - Angular velocity of the rigid body - Distance from the axis of rotation on the body v = lr x ω ω must be converted from deg/sec to rad/sec

Inertia

A resistance to change in motion, specifically a resistance to change in a body's velocity - Applies to: Bodies at rest Bodies moving linearly bodies rotating

Plane

A smooth, flat space defined by two axes

Parabola

A type of plane curve

Resultant

A vector that is equivalent to the combined effect of two or more vectors

Gravity

Acceleration of a body due to the force of gravity; attraction between two objects, for projectile motion, the Earth and a person/object

Cosine (cos)

Adjacent/Hypotenuse

Velocity

Amount of displacement in a given time

Momentum (L)

An object's linear inertia (L) must include: - Mass (m) - Linear velocity (v) A resistance to change in velocity of a moving body "Quantity of motion" L = m(v)

Projectile

Any airborne body that is only subjected to gravity and wind resistance after it has left the ground

Planar

Any motion in plane

Zero

At the apex, the instantaneous Yv is ?

- Gravity alters the path of the projectile in the vertical (y) direction - The magnitude of the alteration is not constant - As time increases, there will be a greater change in the trajectory - The relationship is not a linear one

Based on gravity we can extract what three key points

Centripetal

Change in direction of the linear velocity Centripetal a = v^2/l^2 = lr(ω^2)

Tangential

Change in magnitude of the linear velocity tan a = lra

Acceleration

Change in velocity in a given time

vf2 = vi2 + 2a∆p

Equation for horizontal or vertical displacement

- Solve for the x and y components - Solve for time from a to b, b to c, and a to c - Solve for horizontal displacement - Solve for vertical displacement

For a Projectile Leaving and Landing at the Same Height

Weight (W)

Force due to gravity - Acts only in the downward, vertical direction - Magnitude of 9.81 m/s^2 times the body's mass Quantity: Vector

- The maximum value along an axis occurs when the vector is parallel to that axis: the angle is 0, and the correction factor is 1 - A larger angle will result in a smaller magnitude of the component parallel to that axis and a larger magnitude of the component perpendicular to that axis - The magnitude of the components will be equal at 45 - The magnitude of the resultant is always larger than the two components

General Rules for Correction Factors

Angular Momentum (H)

H = I x (ω)

Angular Speed

How fast a body is rotating Quantity: Scalar

Angular Velocity (ω)

How fast a body is rotating in a particular direction The rate at which angular position changes ω = ∆Ɵ/ ∆t = Ɵ' - Ɵ/ t' - t Quantity: Vector Typical unit: °/s or rad/s

Angular acceleration (α)

How quickly a body is speeding up or slowing down its rotation in a particular direction Time rate of change of angular velocity α = ∆ω/∆t = ω'-ω/ t'-t Quantity: Vector Typical unit: °/s2 or rad/s2

Dynamic

Moving - Mass X Velocity = Inertia (Momentum)

Static

Not moving - Mass = inertia

Constant Acting downward (negative) = -9.81 m/s^2 = -32 ft/s^2

On Earth gravity is ?

57.3 degrees (180/pi)

One radian = ?

Tangent (tan)

Opposite/Adjacent

Sine (sin)

Opposite/Hypotenuse

Three-dimensional

Our world is ?

Component

Parts of a resultant vector; two or more vectors that are acting in different directions

Radius of gyration

Represents the object's mass distribution with respect to a given axis of rotation K is the distance known as ?

Angular

Rotational - Moment of inertia x angular velocity (angular momentum)

Clockwise

Rotations are negative

Counterclockwise

Rotations are positive

Mass (m)

The amount of matter in an object - the amount of "stuff" in an object - Direct relationship with resistance to change in motion - Quantity: Scalar

Moment of Inertia (I)

The angular equivalent of mass Gives an indication of how difficult it will be to rotate an object Explains how the mass is distributed relative to the axis of rotation I = mp2 I = mk2

Angular Displacement (∆Ɵ)

The change in orientation of a rigid body in reference to some axis - Change in angular position between two time periods of interest ∆Ɵ = Ɵ' - Ɵ

Apex

The highest point of a trajectory

Range

The horizontal displacement of a projectile

Angular Position (Ɵ)

The orientation of a rigid body in reference to some axis. It can be measured in degrees (°), radians (rads)

Trajectory

The path of a projectile

Correction factor

The sine or cosine acts as that ______________

Not Constant

The velocity due to gravity is ?

Perpendicular

The velocity vector will always be __________________ to the rigid body

Height

The vertical displacement of a projectile

Tangential Centripetal

Two kinds of linear velocity

- Initial position - Initial velocity - Net acceleration - Change in time

What are the determinants of the final position?

Correct for it

When a vector is not parallel to an axis you must ______________ ____________ ____