One end of a cord is fixed and a small 0.610 kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.00 m as shown in the figure below. When θ = 18.0°, the speed of the object is 4.50 m/s. At this instant, find each of the following.

if they ask find the total acceleration inward and below the cord at? When i find the angle for this, do i take arctan(centripetal accel/tangantial accel) or arctan(tang accel/cent accel)

To find the total acceleration inward and below the cord, you need to use the components of acceleration: centripetal acceleration (radial inward acceleration) and tangential acceleration (horizontal acceleration).

The centripetal acceleration (ac) is directed towards the center of the circular motion and can be calculated using the formula:

ac = (v^2) / r

where v is the speed of the object (4.50 m/s) and r is the radius of the circle (2.00 m).

ac = (4.50^2) / 2.00 = 10.125 m/s^2

The tangential acceleration (at) is directed tangentially in the horizontal direction and can be calculated using the formula:

at = aθ * r

where aθ is the angular acceleration and r is the radius of the circle.

To find aθ, you can use the equation:

aθ = (v^2) / r

Substituting the given values:

aθ = (4.50^2) / 2.00 = 10.125 m/s^2

Now, you can calculate the tangential acceleration:

at = aθ * r = 10.125 * 2.00 = 20.25 m/s^2

So, the centripetal acceleration is 10.125 m/s^2 and the tangential acceleration is 20.25 m/s^2.

To find the angle, you can use the equation:

θ = arctan(at / ac)

Substituting the values:

θ = arctan(20.25 / 10.125) = arctan(2) ≈ 63.4°

So, the angle is approximately 63.4°.

In summary, for the total acceleration inward and below the cord, the centripetal acceleration is 10.125 m/s^2 and the tangential acceleration is 20.25 m/s^2. The angle can be found using the arctan(at / ac) formula, which gives approximately 63.4°.

To find the total acceleration inward and below the cord, you will need to find the components of acceleration: the centripetal acceleration (ac) and the tangential acceleration (at).

In this case, the centripetal acceleration (ac) points towards the center of the circle and helps keep the object moving in a curved path. The tangential acceleration (at) is perpendicular to the centripetal acceleration and points along the tangent to the circle at that point.

To find the angles for these components, you can use trigonometry. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is tangential acceleration (at) and the adjacent side is centripetal acceleration (ac).

So, to find the angle for the total acceleration inward and below the cord, you would use the arctan(tangential acceleration / centripetal acceleration), which is arctan(at / ac).

Keep in mind that the total acceleration will be the vector sum of the centripetal and tangential accelerations. The direction can be found using vector addition techniques.

Hope this helps!