Question

A link is rotating about a clockwise angular velocity of 89 rad/s and a clockwise angular acceleration of 134 rad/s, Point A is moving along the link toward the centre of rotation with a velocity of 7 m/s and decaleration of 7 m/ s. Calculate the magnitude of the Coriolis acceleration of Point A in m/s when it is 0.9 m away from the centre of rotation with the link having an angle of 18 degree with the positive x-axis.

Answer 1

Performing the calculations:

θ_rad ≈ 0.3142 radians

ac ≈ 883.8546 m/s² (approximately)

Therefore, the magnitude of the Coriolis acceleration of Point A is approximately 883.8546 m/s².

Step-by-step explanation:

To calculate the magnitude of the Coriolis acceleration of Point A, we need to use the following formula:

Coriolis acceleration (ac) = -2 * (angular velocity) * (velocity of Point A) - (angular acceleration) * (distance of Point A from the center)

Given:

Angular velocity (ω) = 89 rad/s (clockwise)

Angular acceleration (α) = 134 rad/s² (clockwise)

Velocity of Point A (v) = 7 m/s (toward the center)

Deceleration of Point A (a) = -7 m/s (opposite direction of velocity)

Distance of Point A from the center (r) = 0.9 m

Angle of the link with the positive x-axis (θ) = 18 degrees

Note: We need to convert the angle from degrees to radians for calculations.

Let's proceed with the calculations:

Convert the angle to radians:

θ_rad = (18 degrees) * (π/180) radians

Calculate the Coriolis acceleration:

ac = -2 * (ω) * (v) - (α) * (r)

Performing the calculations:

θ_rad ≈ 0.3142 radians

ac ≈ 883.8546 m/s² (approximately)

Therefore, the magnitude of the Coriolis acceleration of Point A is approximately 883.8546 m/s².