The angular speed of a particle, moving in a circle of radius 20 cm, increases from 2 rad/s to 40 rad/s in 9s. The ratio of its centripetal acceleration to tangential acceleration at the end of 19s is:
Correct answer: C. 800:1
- A. 400:1
- B. 14:20
- C. 800:1
- D. 7:40
Explanation
r= 0.2 m Wo= 2rad/s Wt= 40 rad/s t= 19sec Tangential acceleration : aT = r {(Wt-Wo)/ t} aT = 0.2 {(40-2)/ 19} aT = 0.2 x 2 aT = 0.4 rad/s^2 Centripetal acceleration: aC = w^2 r aC = (40)^2 (0.2) aC = 320 m/s^2 Centripetal : Tangential aC:aT = aC/aT 320 / 0.4 = 800 Thus the ratio will become 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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