Answer:
a = -0.8 m/s²
Here, negative sign indicates that the acceleration has opposite direction to the direction of motion.
Explanation:
First we find the angular acceleration of the ball from the following formula:
α = (ωf - ωi)/t
where,
α = angular acceleration = ?
ωf = final angular velocity = 7 rad/s
ωi = initial angular velocity = 13 rad/s
t = Time taken = 15 s
Therefore,
α = (7 rad/s - 13 rad/s)/15 s
α = - 0.4 rad/s
negative sign shows that acceleration is in opposite direction to the direction of motion.
Now, for the linear acceleration, we use the formula:
a = rα
where,
a = linear acceleration = ?
r = radius of circular path = length of rope = 2 m
therefore,
a = (2 m)(- 0.4 rad/s²)
a = -0.8 m/s²
Here, negative sign indicates that the acceleration has opposite direction to the direction of motion.
