Question

An object moves uniformly around a circular path of radius 19.0 cm, making one complete revolution every 2.40 s.

a. What is the translational speed of the object?
b. What is the frequency of motion inhertz.
c. What is the angular speed of the object?

Answer 1

v = 0.5 m/s

f = 0.42 Hz

ω = 2.6 rad/sec

Step-by-step explanation:

• By definition, the translational speed is the rate of change of the position with respect to time.
• The change in position along a complete revolution is just the following:
• Δs = 2*π*r = 2*π*0.19 m = 1.19 m
• The time needed to complete a revolution is 2.4 s, so the translational speed can be written as follows:

`v =(\Delta s)/(\Delta t) = (1.19m)/(2.4s) = 0.5 m/s (1)`

• The frequency in Hz is just the inverse of the time needed to complete a revolution (known as the period T), as follows:
• f = 1/T = 1/2.4s = 0.42 Hz (2)
• Finally, the angular speed is the rate of change of the angle rotated with respect to time, as follows:

`\omega = (\Delta\theta)/(\Delta t) = (2*\pi)/(2.4s) = 2.6 rad/sec (3)`