If an object moves in uniform circular motion in a circle of radius r = 1.0 meter, and the object takes 4.0 seconds to complete ten revolutions, calculate the centripetal acceleration.

= 246.49 m/s²

Explanation:

We apply the equations of uniform circular motion :

ω= θ/t   Formula (1)

= ω²*R  Formula (2)

Where:

θ : angle that the object travels (rad)

ω: angular velocity ( rad/s)

t : time (s)

: centripetal acceleration (m/s²)

R: radius (m)

Equivalence

1  revolution = 2π radianes =2π rad

Data

θ = ten revolutions =  10* 2π rad = 20π rad

t = 4.0 seconds = 4 s

R = 1.0 meter = 1 m

Problem development

We replace data in  Formula (1)  to calculate ω:

ω = 20π rad / 4 s

ω = 20π rad / 4 s = 15.7 rad / s

We replace data in  Formula (1)  to calculate the centripetal acceleration ;

= ( 15.7 rad /s )² * 1 m

= 246.49 m/s²

it has to be b, about 97 percent.