Question

A stone tied to the end of a string 80cm long is whirled in a horizontal circle with a constant speed.(i) What is the angle between the velocity and acceleration at any instant of motion?
(ii) If the stone makes 14 revolutions in 25s, what is the magnitude of acceleration of the stone?

Answer 1

Answer:

A stone tied to the end of a string 80cm long is whirled in a horizontal circle with a constant speed. This is a case of uniform circular motion.

(i) The angle between the velocity and acceleration at any instant of motion is always 90⁰ in uniform circular motion.

(ii) If the stone makes 14 revolutions in 25s,

radius of circle, r = 80cm = 0.8m

angle covered, Ф = 14×2π = 28π

time, t = 25s

angular speed, ω = Ф/t = 28π/25 = 3.52 rad/s

acceleration, α = ω²r = 3.52² × 0.8 = 9.91 m/s²