The diagram above depicts a system with four axles. Axles B and C have two pulle
ID: 2134740 • Letter: T
Question
The diagram above depicts a system with four axles. Axles B and C have two pulleys of different radii, while axles A and D have only one. The pulley on axle A rotates in the positive direction, 1.9 thousand times every minute. It is connected by a belt to the smaller pulley on axle B. The larger pulley on axle B is spinning directly against the smaller pulley on axle C. The larger pulley on axle C is connected to the pulley on axle D by a belt. All pulleys are bolted into their respective axles - a pulley can't "slip" in angle with respect to another pulley on the same axle. There is no slipping on the different connections between the axles either.
The largest pulley in the system is on axle B. Its diameter is is 1.8 times larger than the diameter of pulley A, and 3.3 times larger than the diameter of the smaller pulley on axle B. The ratio of diameters of the pulleys on axle C is 1 : 1.9. The diameter of pulley D is 1.3 times larger than the diameter of the smaller pulley on Axle B.
What is the angular velocity of pulley D in rad/sec, using the standard definition of positive angle?
The angular velocity of pulley D is rad/sec.
The diagram above depicts a system with four axles. Axles B and C have two pulleys of different radii, while axles A and D have only one. The pulley on axle A rotates in the positive direction, 1.9 thousand times every minute. It is connected by a belt to the smaller pulley on axle B. The larger pulley on axle B is spinning directly against the smaller pulley on axle C. The larger pulley on axle C is connected to the pulley on axle D by a belt. All pulleys are bolted into their respective axles - a pulley can't "slip" in angle with respect to another pulley on the same axle. There is no slipping on the different connections between the axles either. The largest pulley in the system is on axle B. Its diameter is is 1.8 times larger than the diameter of pulley A, and 3.3 times larger than the diameter of the smaller pulley on axle B. The ratio of diameters of the pulleys on axle C is 1 : 1.9. The diameter of pulley D is 1.3 times larger than the diameter of the smaller pulley on Axle B.Explanation / Answer
Vba = Wa Ra
Wa = 1900 / 60 * 2 * pi * = 199 rad/sec angular speed of A
Vba = Wa Ra = Wb Rxb speed of belt on A and axle of B
Vrb = Wb Rb speed of rim of B
Vrb = (Wa Ra / Rxb) Rb
Rb = 1.8 Ra = 3.3 Rxb
Ra / Rxb = 1.83 Rb = 1.8 Ra
Vrb = Wa * 1.83 * 1.8 Ra = 3.29 Wa Ra speed of rim of B
Vxc = Vrb = Wc Rxc speed of rim of axle on C
Wc = Vrb / Rxc
Vrc = Wc * Rc = Vrb * Rc / Rxc = 3.29 Wa Ra * 1.9 = 6.25 Wa Ra
Vrc = Wd Rd speed of rim of C = speed of rim of D
6.25 Wa Ra = Wd Rd
Wd = 6.25 Wa Ra / Rd = 1243 Ra / Rd angular speed of D
D will be rotating oppositely to A
Rb = 1.8 Ra = 3.3 Rxb
Rd = 1.3 Rxb
Ra = 3.3 Rxb / 1.8 = 3.3 Rd / (1.3 * 1.8) = 1.41 Rd
Wd = 1243 * 1.41 = -1753 rad/sec