Question

At a playground a student runs at a speed of 5 m/s and jump onto a circular disk of radius 3/2 m that is free to rotate around a fixed vertical axle. The student jumps on the disk several times, and the angular speed after the student lands is measured each time. Which of the following angular speeds is not a reasonable value for the measured angular speed?
a. 0.5 rad/s
b. 1 rad/s
c. 2 rad/s
d. 3 rad/s
e. 4 rad/s

Answer 1

Answer:

e. 4 rad/s

Explanation:

The maximum amount of angular velocity that can be reached by the disk can be found using the following formula:

$v = r\omega\\\\\omega = \frac{v}{r}$

where,

ω = maximum angular velocity = ?

v = linear speed = 5 m/s

r = radius of disc = 1.5 m

Therefore,

$\omega = \frac{5\ m/s}{1.5\ m} \\\\\omega = 3.33\ rad/s$

Therefore, the angular speed can be lower than this value due to frictional losses, but it can not exceed this value in the given linear speed limit of 5 m/s.

Hence, the correct option is:

e. 4 rad/s