Respuesta :
r = radius of the circle traveled by the particle = 76 cm = 0.76 m
T = time period of revolution for the particle = 4.5 s
w = angular velocity of the particle
angular velocity of the particle is given as
w = 2π/T
inserting the values
w = 2 (3.14)/4.5
w = 1.4 rad/s
a = centripetal acceleration of the particle in the circle
centripetal acceleration is given as
a = r w²
inserting the values
a = (0.76) (1.4)²
a = 1.5 m/s²
Answer:
Acceleration, [tex]a=1.12\ m/s^2[/tex]
Explanation:
Given that,
Radius of circle, r = 76 cm = 0.76 m
Time period of revolution, t = 4.5 s
To find :
Centripetal acceleration of the particle.
Solution,
Let v is the velocity of particle. On the circular path velocity of a particle is given by :
[tex]v=\dfrac{2\pi r}{t}[/tex]
The centripetal force on the circular path is given by:
[tex]a=\dfrac{v^2}{r}[/tex]
[tex]a=\dfrac{(\dfrac{2\pi r}{t})^2}{r}[/tex]
[tex]a=\dfrac{4\pi^2 r^2}{t^2}[/tex]
[tex]a=\dfrac{4\pi^2 (0.76)^2}{(4.5)^2}[/tex]
[tex]a=1.12\ m/s^2[/tex]
So, the acceleration of the particle is [tex]1.12\ m/s^2[/tex].
