1 / 8

w 1

y. w 1. A. z. x. b. B. Problem 15.259. Rod AB of length 125 mm is attached to a vertical rod that rotates about the y axis at the constant rate w 1 = 5 rad/s. Knowing that the angle formed by rod AB and the vertical is increasing at the

vic
Download Presentation

w 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. y w1 A z x b B Problem 15.259 Rod AB of length 125 mm is attached to a vertical rod that rotates about the y axis at the constant rate w1 = 5 rad/s. Knowing that the angle formed by rod AB and the vertical is increasing at the constant rate db/dt = 3 rad/s, determine the velocity and acceleration of end B of the rod when b = 30o.

  2. Problem 15.259 y w1 A z x b B w w2 O w1 Solving Problems on Your Own Rod AB of length 125 mm is attached to a vertical rod that rotates about the y axis at the constant rate w1 = 5 rad/s. Knowing that the angle formed by rod AB and the vertical is increasing at the constant rate db/dt = 3 rad/s, determine the velocity and acceleration of end B of the rod when b = 30o. 1. To determine the velocity and acceleration of a point of a body rotating about a fixed point: 1a. Determine the angular velocity w of the body: The angular velocity w with respect to a fixed frame of reference is often obtained by adding two component angular velocities w1 and w2.

  3. Problem 15.259 y w1 A z x b B Solving Problems on Your Own Rod AB of length 125 mm is attached to a vertical rod that rotates about the y axis at the constant rate w1 = 5 rad/s. Knowing that the angle formed by rod AB and the vertical is increasing at the constant rate db/dt = 3 rad/s, determine the velocity and acceleration of end B of the rod when b = 30o. 1b. Compute the velocity of a point of the body: The velocity v of point B in the body is given by: v = wxr where r is the position vector connecting the fixed point O to point B. w B r O

  4. Problem 15.259 y w1 A z x b B Solving Problems on Your Own Rod AB of length 125 mm is attached to a vertical rod that rotates about the y axis at the constant rate w1 = 5 rad/s. Knowing that the angle formed by rod AB and the vertical is increasing at the constant rate db/dt = 3 rad/s, determine the velocity and acceleration of end B of the rod when b = 30o. 1c. Determine the angular acceleration a of the body: a = ( w )OXYZ = (w )oxyz + Wxw a is the rate of change (w)OXYZ of the vector w w.r.t. a fixed frame of reference OXYZ, (w)oxyz is the rate of change of w w.r.t. a rotating frame of reference oxyz, W is the angular velocity of the rotating frame . . . . Y y w a . W x o O X Z z

  5. Problem 15.259 y w1 A z x b B Y y w a r x o Z O X z Solving Problems on Your Own Rod AB of length 125 mm is attached to a vertical rod that rotates about the y axis at the constant rate w1 = 5 rad/s. Knowing that the angle formed by rod AB and the vertical is increasing at the constant rate db/dt = 3 rad/s, determine the velocity and acceleration of end B of the rod when b = 30o. 1d. Compute the acceleration of a point of a body: aB = axrB/A + wx(wxrB/A) Where aB is the acceleration of point B, aA is the (known) acceleration of point A, a and w are the angular acceleration and angular velocity of the body with respect to a fixed frame of reference, and rB/A is the position vector of B relative to A.

  6. y Problem 15.259 Solution ijk 0 5 3 0.0625 -0.1083 0 Determine the angular velocity of the body. w1 w1 = 5 j rad/s w2 = db/dt= 3 rad/s, w2 = 3 k rad/s w = w1 + w2 = 5 j + 3 k rad/s A z w2 x Compute the velocity of a point of the body. b B The velocity of end B: For b = 30o and rB/A = 0.125 rB/A = 0.125 sin30oi - 0.125 cos30oj = 0.0625 i - 0.1083 j vB = w x rB/A = vB = 0.325 i + 0.188 j - 0.313 k m/s

  7. y Problem 15.259 Solution Y w1 w2 o A Z O z x X b B Determine the angular acceleration a of the body. Frame OXYZ is fixed. Frame oxyz is attached to the vertical rod and rotates with constant angular velocity w1. . Consequently: w1= 0 and W = w1 . . . . a = w = w1 + w2 = 0 + w2 . . a = ( w2 )OXYZ = (w2)oxyz + Wxw2 a = 0 + a = 15 i rad/s2 ijk 0 5 0 0 0 3

  8. y Problem 15.259 Solution ij k 0 5 3 0.325 0.188 -0.313 ijk 15 0 0 0.0625 -0.108 0 aB = + aB = -2.13 i + 0.97 j - 3.25 k m/s2 Compute the acceleration of a point of a body. w1 The acceleration of end B: w = 5 j + 3 k rad/s Recall: A a = 15 i rad/s2 z rB/A = 0.0625 i - 0.1083 j w2 x b vB = wxrB/A = 0.325 i + 0.188 j - 0.313 k m/s B aB = axrB/A + w x(wxrB/A) aB = axrB/A + w xvB

More Related