Question

Allison twirls and umbrella around its centripetal axis so that it completes 26.0 rotations in 30s. If the acceleration is constant and the radius of the umbrella is 51.0 cm, what is the maximum tangential speed of a point on the edge?

Answer 1

To find the maximum tangential speed of a point on an umbrella's edge during twirling, calculate the angular velocity and then use it with the radius to determine the speed. The maximum tangential speed is found to be 2.777 m/s.

Step-by-step explanation:

The student is asking about the maximum tangential speed of a point on the edge of an umbrella being twirled around its centripetal axis. Given the umbrella completes 26.0 rotations in 30 seconds and has a radius of 51.0 cm, we need to calculate the angular velocity and then use it to find the tangential speed. The angular velocity (ω) can be found by using the formula ω = (2π*number of rotations) / time, which gives us the angular velocity in radians per second. Then, the maximum tangential speed (vt) is calculated using vt = r*ω, where r is the radius.

To solve this problem:

1. First, convert the rotations into radians: 26 rotations * 2π rad/rotation = 163.36 radians.
2. Next, calculate angular velocity: ω = 163.36 radians / 30 s = 5.445 rad/s.
3. Finally, calculate tangential speed: vt = 0.51 m * 5.445 rad/s = 2.777 m/s.

Therefore, the maximum tangential speed of a point on the edge of the umbrella is 2.777 m/s.