Topic: Theory of Machines
A slider moving outward on a rod OR with a velocity of 3 m/s and acceleration of 9 m/s². The rod has an angular velocity of 7 rad/s counter clockwise about O and an angular acceleration of 12 rad/s² clockwise. The magnitude of absolute acceleration of the slider at location A in m/s² is (where OA = 1m)
- A. 20
- B. 50
- C. 67
- D. 79
Answer: B. 50
Explanation: Radial acceleration ar = d^2r/dt² - r*omega² = 9 - 1*(7^2) = 9 - 49 = -40 m/s². Tangential acceleration at = r*alpha + 2*(dr/dt)*omega = 1*(-12) + 2*3*7 = -12 + 42 = 30 m/s². Absolute acceleration = $\sqrt{ar² + at²}$ = $\sqrt{(-40}$^2 + 30^2) = 50 m/s².