Question

A typical ten-pound car wheel has a moment of inertia of about 0.35 kg·m². The wheel rotates about the axle at a constant angular speed, making 30.0 full revolutions in a time interval of 5.00 s. What is the angular speed of the wheel?

a) 6 rad/s
b) 4 rad/s
c) 2 rad/s
d) 1.5 rad/s

Answer 1

To calculate the angular speed, multiply the number of revolutions by 2π to get the angular displacement in radians, then divide by the time in seconds. The answer does not match the provided options, indicating a possible error in the question or answer choices.

Step-by-step explanation:

The question asks us to determine the angular speed of a car wheel given the number of revolutions it makes over a specific time interval. Angular speed (ω) can be calculated using the formula ω = θ / t, where θ is the angular displacement in radians and t is the time in seconds.

Since one revolution corresponds to 2π radians, we can convert 30.0 revolutions into radians by multiplying 30.0 by 2π. Therefore, θ = 30.0 revolutions * 2π radians/revolution = 60π radians. Given that the wheel makes this many revolutions in 5.00 seconds, we can now calculate the angular speed.

ω = θ / t = 60π radians / 5.00 s = 12π radians/s. Converting this into decimal form, ω ≈ 37.7 rad/s. However, this value does not match any of the provided options, suggesting there might be a typo in the question or the options given.

None of the options (a) 6 rad/s, (b) 4 rad/s, (c) 2 rad/s, (d) 1.5 rad/s are correct based on the calculation with the provided information.