Respuesta :
Answer:
(1) The period 0.25 secs
(2) The angular velocity is 25.14 rad/s
(3) The linear velocity is 50.28 m/s
(4) The acceleration is [tex]1264 m/s^{2}[/tex]
Explanation:
(1) Period is defined as the time taken for one revolution
∴ [tex]Period = \frac{Time }{Number of revolutions }[/tex]
From the question, the particle makes 240 revolution per minute
That is, For 240 revolution, the time taken = 1 minute
Time = 1 minute = 60 secs
Number of revolutions = 240
∴ [tex]Period =\frac{60}{240} \\[/tex]
Period = 0.25 secs
The period 0.25 secs
(2) The angular velocity, ω is given by
ω [tex]= \frac{2\pi }{T} \\[/tex]
where [tex]T[/tex] is the period
∴ω = 2 ×[tex]\frac{22}{7}[/tex] / 0.25 (take [tex]\pi = \frac{22}{7}[/tex])
ω = 25.14 rad/s
The angular velocity is 25.14 rad/s
(3) The linear velocity, v is given by
v = ωr
Where v is the linear velocity
ω is the angular velocity
and r is the radius
From the question, r = 2m
From v = ωr
∴v = 25.14 × 2
v = 50.28 m/s
The linear velocity is 50.28 m/s
(4) The acceleration is given by
[tex]a =[/tex] ω × v = ω(ωr) =ω²r
∴ [tex]a = 25.14^{2}[/tex] × [tex]2[/tex]
[tex]a = 1264.04 m/s^{2} \\a = 1264 m/s^{2}[/tex]
The acceleration is [tex]1264 m/s^{2}[/tex]
