Motion of a firefighter on a ladder. (Understanding definitions - Section 8.1)
The following figure shows a fire truck chassis A traveling at a constant speed in straight-line motion on Earth (A does not rotate relative to Earth). Earth is a Newtonian reference frame N. A rigid hub B is connected to fire truck A by a revolute motor at point B. A rigid ladder C is connected to hub B by a revolute motor at point Co of C. A firefighter Q (modeled as a particle of mass m) climbs ladder C. Right-handed orthogonal unit vectors ax, ay, and az are fixed in A, B, and C, with ax pointing forward on the fire truck, ay vertically upward, and az from B to C.
By parallel to the axis of the revolute motor that connects B and A, b = ay. C parallel to the axis of the revolute motor that connects B and C, Cx directed from Co to Q along C's long axis. Note: Visualize C's Body yz (or Space zy) rotation sequence in N (e.g. with a ruler).
Symbol Type:
Since A is not rotating in N, NA = 0.
Quantity UA: Constant
Since NA = Aax is constant in N, a measure of A's velocity in N.
WB: Constant
NaA = 0. Hence, every point of A has 0 acceleration in N. Thus, A is also a Newtonian reference frame.
C: Measure of Q's position vector from C.
Use definitions to form the following quantities:
Note: Rotational kinematics are in Homework 6.9.
9/C = xCx + 20e = cx + 22 + 2 + 22
B = Ba9 = C + x2 + hCy + 32
AQ = AQ = Cx + k + NQ = NO = x + B Cx + cy + 22