polar_kinematics

polar_kinematics - 3 ( ) 2 ( ) 2 = 12 meters r = 3 2 ( ) =...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Using a Polar Description in Kinematics The position, velocity and acceleration of a point P using a polar kinematical description are given by: r P = re r v P = ˙ r e r + r ˙ " e a P = ˙ ˙ r " r ˙ # 2 ( ) e r + r ˙ ˙ + r ˙ ( ) e where e r and e are the polar unit vectors, as shown below. Note that e r points from the fixed origin O toward P. e is perpendicular to e r with the same positive sense as the defined angle θ . Example Point P travels on a path described by r = 3 2 (r is measured in meters and θ in radians). If ˙ = 3 rad / sec = constant what is the speed and magnitude of acceleration of P when = 2radians . Solution r = 3 2 =
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3 ( ) 2 ( ) 2 = 12 meters r = 3 2 ( ) = 3 ( ) 2 ( ) 2 ( ) 3 ( ) = 36 m / sec r = 6 2 + ( ) = 6 3 ( ) 2 + 2 ( ) ( ) [ ] = 54 m / sec 2 Therefore, v P = r e r + r e = 36e r + 12 ( ) 3 ( ) e = 36e r + 36e ( ) m / sec # v P = 36 ( ) 2 + 36 ( ) 2 = 36 2 m / sec a P = r " r 2 ( ) e r + r + 2 r ( ) e = 54 " 12 ( ) 3 ( ) 2 [ ] e r + 12 ( ) ( )+ 2 36 ( ) 3 ( ) [ ] e = " 54e r + 216e ( ) m / sec 2 $ a P = 54 ( ) 2 + 216 ( ) 2 m / sec 2 r P O e r e...
View Full Document

Ask a homework question - tutors are online