Question

Allison twirls and umbrella around its centripetal axis so that it completes 26.0 rotations in 30s. What is the angular velocity of the umbrella?

1) 0.87 rad/s
2) 0.87 Hz
3) 0.87 rpm
4) 0.87 degrees/s

Answer 1

The angular velocity of the umbrella is approximately 5.4 rad/s when she completes 26.0 rotations in 30 seconds. None of the answer options provided is correct.

Step-by-step explanation:

To calculate the angular velocity of the umbrella, we need to use the formula for angular velocity, ω = Δθ / Δt, where Δθ is the change in angle measured in radians and Δt is the change in time. Given that the umbrella completes 26.0 rotations in 30 seconds, and one rotation is equivalent to 2π radians, we first find the total angle rotated, Δθ = 26.0 rotations × 2π radians/rotation. Then, we divide this by the time of 30 seconds to find the angular velocity.

Δθ = 26.0 × 2π = 52π radians

ω = 52π radians / 30s ≈ 5.4 radians/s

Therefore, none of the given options (0.87 rad/s, 0.87 Hz, 0.87 rpm, 0.87 degrees/s) are correct. The angular velocity of the umbrella is approximately 5.4 rad/s.