What is the speed of the professor's hands in meters per second?
To find the speed of the professor's hands, we need to convert her spinning rate to radians per second and then multiply this by the distance from the axis of rotation to her hands. The final answer is approximately 0.84 m/s.
Understanding Rotational Motion and Angular Kinetics
RPM to Radians per Second Conversion: The spinning rate of the professor is given as 10.0 rpm. To convert this to radians per second, we use the conversion factor 1 rev = 2π rad. Therefore, the angular speed ω is calculated as 10.0 rpm * (2π rad) / (60 sec) ≈ 1.047 rad/s.
Calculation of Speed of Professor's Hands:
Formula: The speed of the professor's hands can be determined using the formula for tangential speed, v = ωr, where 'v' represents the linear speed of the hands, 'ω' is the angular speed, and 'r' is the distance from the axis of rotation to the hands.
Substitute the values of angular speed (ω ≈ 1.047 rad/s) and distance (r = 0.805 m) into the formula: v = 1.047 rad/s * 0.805 m ≈ 0.84 m/s.
Therefore, the speed of the professor's hands while holding the weights on a rotating stool spinning at 10.0 rpm is approximately 0.84 m/s.