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Two go-karts race around a course that has concentric circular tracks. The radius of the inner track is 15.0 m, and the radius of the outer track is 19.0 m. The go-karts start from rest at the same angular position and time, and move at the same constant angular acceleration. The race ends in a tie after one complete lap, which takes 21.5 seconds. (a) What is the common angular acceleration of the carts? (b) What is the tangential acceleration of the inner cart? (c) What is the tangential acceleration of the outer cart?

Added Tue, 04 Aug '15

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Angular acceleration = (Increase of angular velocity) � time

Angular velocity = number of radians per second.

Initial angular velocity = 0 rad/s

Both karts move 1 circle in 21.5 seconds. 1 circle = 2 * ? radians

Final angular velocity = 2 * ? � 21.5

Increase of angular velocity = (2 * ? � 21.5) rad/s

Angular acceleration = (2 * ? � 21.5) � 21.5 = 0.0136 rad/s

The tangential acceleration is actually the centripetal acceleration.

Centripetal acceleration = velocity^2 � radius

The carts are traveling at constant speed. The distance which kart moves in, 21.5 seconds, is the circumference of the circle.

Speed of the kart = circumference � 21.5

Circumference of inner track = 2 * ? * 15, speed = 2 * ? * 15 � 21.5

Centripetal acceleration = (2 * ? * 15 � 21.5)^2 � 15 = 1.28 m/s^2

For the kart on the inner track, tangential acceleration = 1.28 m/s^2

Circumference of outer track = 2 * ? * 19, speed = 2 * ? * 19 � 21.5

Centripetal acceleration = (2 * ? * 19 � 21.5)^2 � 19 = 1.62 m/s^2

For the kart on the inner track, tangential acceleration = 1.62 m/s^2

Added Tue, 04 Aug '15

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