Question

If the angular velocity of a wheel is 40 rad/s, and the wheel radius is 30 cm, what is the tangential velocity?

a) 12 cm/s
b) 240 cm/s
c) 1.5 cm/s
d) 24 cm/s

Answer 1

To find the tangential velocity of a wheel with an angular velocity of 40 rad/s and a radius of 30 cm, use the formula v = r⋅ω. The result equals 12 m/s or 1200 cm/s, which doesn't match any of the provided options, suggesting a mistake in the options given.

Step-by-step explanation:

If the angular velocity of a wheel is 40 rad/s, and the wheel radius is 30 cm, you can calculate the tangential velocity by using the formula v = r⋅ω, where v is the tangential velocity, r is the radius, and ω is the angular velocity. Substituting the given values:

v = 0.30 m ⋅ 40 rad/s = 12 m/s

Since the question provides options in centimeters per second, we convert meters per second to centimeters per second:

v = 12 m/s ⋅ 100 cm/m = 1200 cm/s

This result does not match any of the provided options, indicating a possible mistake with the options. The correct tangential velocity would be 1200 cm/s, assuming the initial data is correct.