Question

A 19-year old soccer player extends their right knee from an initial angle of 20o to 140o in 2 s. If this movement began from rest, what was the angualr acceleration? Hint: convert angular displacement to radians (1 revolution = 360o = 2π radians).

Answer 1

Answer: 32π/9 rad/s²

Explanation: initial angular displacement = 20°, final angular displacement = 140°, average time = 2s.

We need to convert the angular displacements to radian.

Recall that 2π = 360°, hence 20° = (20 × 2π)/360 = π/9 rad

Converting 140° to radian we have that

140° = (140 × 2π)/360 = 7π/9

Initial angular displacement = π/9 rad

Final angular displacement = 7π/9

Average angular velocity = change in angular displacement /time

Average angular velocity = 7π /9 - π/9/2

Average angular velocity = (8π/9)/2

Average angular velocity = 16π/9 rad/s

Average angular acceleration = average angular velocity / time taken

Average angular acceleration = (16π/9)/2

Average angular acceleration = 32π/9 rad/s²