The angular speed of a particle moving in a circle of radius 20 cm, increases from 2 rad/s to 40 rad/s in 19s. What is the ratio of its centripetal acceleration to tangential acceleration at the end of 19s?
Correct answer: C. 800:1
- A. 400:1
- B. 14:20
- C. 800:1
- D. 7:40
Explanation
Initial angular speed of the particle, ω1 = 2 rad/s Final angular speed of the particle, ω2 = 40 rad/s Radius of the circle, r = 20 cm = 0.2 m Time taken, t = 19 s Centripetal acceleration at the end of 19s, ac = ω22 x r ac = (40)2 x 0.2 ac = 320 m/s2 Tangential acceleration at the end of 19s, at = r x α Where α is Angular acceleration, which can be written as α = (ω2 - ω1) / t Now, at = 0.2 x ((ω2 - ω1) / t) at = 0.2 x ((40 - 2) / 19) at = 0.2 x 2 at = 0.4 m/s2 The ratio of centripetal acceleration to tangential acceleration at the end of 19s is: ac / at = 320 / 0.4 = 800:1 Hence, the answer is (C) 800:1.
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About Angular and Linear Quantities
Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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