Objective

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# Objective - PowerPoint PPT Presentation

Objective. To investigate particle motion along a curved path “ Curvilinear Motion ” using three coordinate systems Rectangular Components Position vector r = x i + y j + z k Velocity v = v x i + v y j + v z k (tangent to path)

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## Objective

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Presentation Transcript

Objective

• To investigate particle motion along a curved path “Curvilinear Motion” using three coordinate systems
• Rectangular Components
• Position vector r = x i + y j + z k
• Velocity v = vx i + vy j + vz k (tangent to path)
• Acceleration a = ax i + ay j +az k (tangent to hodograph)
• Normal and Tangential Components
• Position (particle itself)
• Velocity v = u ut (tangent to path)
• Acceleration (normal & tangent)
• Polar & Cylindrical Components
Curvilinear Motion: Cylindrical Components
• Section 12.8
• Observed and/or guided from origin or from the center
• Cylindrical component
• Polar component “plane motion”
Polar Coordinates
• Transverse coordinate
• q and r are perpendicular
• Direction ur and uq
Position
• Position vector
• r = r ur
Velocity
• Instantaneous velocity = time derivative of r
• Where
Velocity (con.)
• Magnitude of velocity
• Angular velocity
• Tangent to the path
• Angle = q + d

d

Acceleration
• Instantaneous acceleration = time derivative of v
Acceleration (con.)
• Angular acceleration
• Magnitude
• Direction “Not tangent”
• Angle q + f

f

Cylindrical Coordinates
• For spiral motion cylindrical coordinates is used r, q, and z.
• Position
• Velocity
• Acceleration

Problem

• The slotted fork is rotating about O at a constant rate of 3 rad/s. Determine the radial and transverse components of velocity and acceleration of the pin A at the instant q = 360o. The path is defined by the spiral groove r = (5+q/p) in., where q is in radians.

Problem

A collar slides along the smooth vertical spiral rod, r = (2q) m, where q is in radians. If its angular rate of rotation is constant and equal 4 rad/s, at the instant q = 90o. Determine

- The collar radial and transverse component of velocity

- The collar radial and transverse component of acceleration.

- The magnitude of velocity and acceleration