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Engr 240 – Week 3

Engr 240 – Week 3. Radial and Transverse Components. Rate of Change of a Unit Vector. where is a unit vector perpendicular to in the direction of increasing. Therefore:. The particle velocity vector is. Radial and Transverse (Polar). Recall:. Particle acceleration vector is.

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Engr 240 – Week 3

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  1. Engr 240 – Week 3 Radial and Transverse Components

  2. Rate of Change of a Unit Vector where is a unit vector perpendicular to in the direction of increasing . Therefore:

  3. The particle velocity vector is Radial and Transverse (Polar) Recall:

  4. Particle acceleration vector is

  5. Example: Rotation of crank OA is controlled by the horizontal slotted link that has a downward acceleration and velocity of 3.5 m/s2 and 0.3 m/s, respectively when θ=30o. For this instant, find the velocity and acceleration of A, and the corresponding values of and .

  6. Sample Problem 11.12 SOLUTION: • Evaluate time t for q = 30o. • Evaluate radial and angular positions, and first and second derivatives at time t. Rotation of the arm about O is defined by q = 0.15t2 where q is in radians and t in seconds. Collar B slides along the arm such that r = 0.9 - 0.12t2 where r is in meters. After the arm has rotated through 30o, determine (a) the total velocity of the collar, (b) the total acceleration of the collar, and (c) the relative acceleration of the collar with respect to the arm. • Calculate velocity and acceleration in cylindrical coordinates. • Evaluate acceleration with respect to arm.

  7. SOLUTION: • Evaluate time t for q = 30o. • Evaluate radial and angular positions, and first and second derivatives at time t.

  8. Calculate velocity and acceleration.

  9. Evaluate acceleration with respect to arm. Motion of collar with respect to arm is rectilinear and defined by coordinate r.

  10. Example. Car B rounds the curve with a constant speed of 90 km/h. If car A has a speed of 60 km/h that is increasing at the rate of 4 km/h each second when the cars are in the position shown, determine the velocity and acceleration of car B relative to car A.

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