How to Calculate Linear Speed, Angular Speed, Period of Rotation, and Frequency of a Rotating Object
a) What is the linear speed of the rotating object at the edge?
a) 7.25 inch circular power saw blade rotates at 5200 revolutions per minute.
b) What is the angular speed of the rotating object in radians per second?
b) 7.25 inch circular power saw blade rotates at 5200 revolutions per minute.
c) What is the period of rotation of the rotating object?
c) 7.25 inch circular power saw blade rotates at 5200 revolutions per minute.
d) What is the frequency of the rotating object's motion?
d) 7.25 inch circular power saw blade rotates at 5200 revolutions per minute.
Answers:
The linear speed of the rotating object's edge is approximately 50.14 m/s.
The angular speed of the blade is 544.49 rad/s.
The period of rotation is 0.0115 seconds.
The frequency of the rotating object's motion is 86.67 Hz.
Explanation:
To answer the questions: Linear Speed: For a rotating object, the linear speed at the edge (v) is the product of the radius (r) and the angular speed (ω). Convert the blade diameter from inches to meters (7.25 inch is 0.18415 m in diameter, so r = 0.092075 m, which is the radius). Convert RPM to radians per second (5200 RPM is 544.49 rad/s). Calculate v = rω = (0.092075 m) * (544.49 rad/s) = 50.14 m/s. Angular Speed: The angular speed of the blade is already given as 544.49 rad/s. Period of Rotation: The period of rotation (T in seconds) is the reciprocal of the frequency in Hz. Convert RPM to frequency (Frequency = 5200 RPM / 60 seconds = 86.67 Hz). Calculate T = 1 / Frequency = 0.0115 seconds. Frequency of the rotating object's motion: This is the frequency calculated in the previous step, which is 86.67 Hz.