Engr Help

Relative Velocity and Acceleration withTranslating and Rotating Frames

Example: Block R slides to the left at a constant speed v_R while a bar B leans against it always

remaining in contact with the bar. Let P be the point in the bar in contact with point S, a point

in the block. The lower end of the bar, Q, has a velocity v_Q i m/sec and an acceleration a_Q i m/sec².

Let xy be a fixed frame of reference with unit vectors i and j . Let x₁y₁ be a translating/rotating

frame with origin at Q attached to the bar with unit vectors i₁ and j₁ . See the figure below.

The following data apply: d = 4 m, h = 3 m, v_R = - 5 m/sec, v_Q = 20 m/sec, a_Q = - 36 m/sec²

Find the velocity of P in the fixed frame of reference F. i.e. v_P|_F

Find the velocity of P relative to the bar in terms of components in the fixed frame.

Find the angular velocity of the bar.

Since P is a point in the bar coincident with S, a point in the block and block R is sliding ,

the velocity of P is ˗ v_R i v_P = ˗ 5 i m/sec (result)

To find the velocity of P relative to the bar and the angular velocity of the bar you need to

apply the general relative velocity equation for a translating/rotating frame of reference.

v_B = v_A + v_B|₁ + ω x r_AB

Relative Velocity Equation

For this example the equation becomes (written for points P and Q )

v_P|_F = v_Q|_F + v_P|_B+ ω_B x r_QP