Question

HOME MY COURSES USEFUL LINKS E ed The pinion gear A rolls on the fixed gear rack B with an angular velocity w = 4 rad/s. Determine the velocity of the gear rack c. 200 ion 0.5 ft. B Select one: 4 m/s 1.2 m/s 8 m/s 2.4 m/s bus page

Answer 1

As the gear Rack B is fixed

Therefore $\overrightarrow{V_{B}}=0$

Using the concept of relative velocity

$\overrightarrow{V_{C}}=\overrightarrow{V_{A}}+\overrightarrow{V_{C/A}}$

Vc = (-rw)i + (-rw)

Since the direction of Both are same, we have represented them with the same unit vectors.Negative sign implies that the direction of velocity is to the left or towards negative X-axis

$\overrightarrow{V_{C}}=(-2rw)\widehat{i}$

Magnitude of V_C is given by

$V_{C} = \sqrt{(-2rw)^{2}}$

V_C = 2 * r * w

Since 1 feet = 0.3048 metres

r= 0.5 feet = 0.5*0.3048 metres = 0.15  metres

V_C = 2 * 0.15 * 4

V_C = 1.2 m/s

Velocity of the gear rack C is 1.2 m/s

Correct option is Option B

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