Question

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

Answer 1

Answer:

v = 0.5 m/s

f = 0.42 Hz

ω = 2.6 rad/sec

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:

        $v =\frac{\Delta s}{\Delta t} = \frac{1.19m}{2.4s} = 0.5 m/s (1)$

• 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:

       $\omega = \frac{\Delta\theta}{\Delta t} = \frac{2*\pi}{2.4s} = 2.6 rad/sec (3)$