A cyclist on a circular track of radius 600 feet is travelling at 36 feet per second. His speed is increased with angular acceleration of 0. 01 rad/sec². What is the cyclist total acceleration?
To find the total acceleration of the cyclist, we need to consider both the tangential acceleration and the centripetal acceleration.
1. Tangential acceleration:
The tangential acceleration is the rate at which the speed of the cyclist is changing. In this case, the angular acceleration is given as 0.01 rad/sec². We can use the formula:
Tangential acceleration = Angular acceleration × radius
Given:
Angular acceleration (α) = 0.01 rad/sec²
Radius (r) = 600 feet
Tangential acceleration = 0.01 rad/sec² × 600 feet
Tangential acceleration = 6 feet/sec²
2. Centripetal acceleration:
The centripetal acceleration is the acceleration towards the center of the circular track and can be calculated using the formula:
Centripetal acceleration = (Speed)² / Radius
Given:
Speed (v) = 36 feet/sec
Radius (r) = 600 feet
Centripetal acceleration = (36 feet/sec)² / 600 feet
Centripetal acceleration ≈ 2.16 feet/sec²
3. Total acceleration:
To find the total acceleration, we need to add the tangential acceleration and the centripetal acceleration.
Total acceleration = Tangential acceleration + Centripetal acceleration
Total acceleration = 6 feet/sec² + 2.16 feet/sec²
Total acceleration ≈ 8.16 feet/sec²
Therefore, the cyclist's total acceleration is approximately 8.16 feet/sec².