Angle of Inclination of Resultant Acceleration with Tangential Acceleration Solution

STEP 0: Pre-Calculation Summary
Formula Used
Inclination Angle = atan(Normal Acceleration/Tangential Acceleration)
Φ = atan(an/at)
This formula uses 2 Functions, 3 Variables
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)
Variables Used
Inclination Angle - (Measured in Radian) - Inclination Angle of the line is the angle which a straight line makes with the positive direction of x-axis measured in the anti-clockwise direction to the part of the line above the x-axis.
Normal Acceleration - (Measured in Meter per Square Second) - Normal Acceleration is the component of acceleration for a point in curvilinear motion that is directed along the principal normal to the trajectory toward the center of curvature.
Tangential Acceleration - (Measured in Meter per Square Second) - Tangential acceleration is defined as the rate of change of tangential velocity of the matter in the circular path.
STEP 1: Convert Input(s) to Base Unit
Normal Acceleration: 6000 Meter per Square Second --> 6000 Meter per Square Second No Conversion Required
Tangential Acceleration: 24 Meter per Square Second --> 24 Meter per Square Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Φ = atan(an/at) --> atan(6000/24)
Evaluating ... ...
Φ = 1.56679634812803
STEP 3: Convert Result to Output's Unit
1.56679634812803 Radian --> No Conversion Required
FINAL ANSWER
1.56679634812803 1.566796 Radian <-- Inclination Angle
(Calculation completed in 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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18 Kinematics Calculators

Angular Displacement given Initial Angular Velocity Angular Acceleration and Time
Go Angular Displacement = Initial Angular Velocity*Time Taken to Travel the Path+(Angular Acceleration*Time Taken to Travel the Path^2)/2
Displacement of Body given Initial Velocity Acceleration and Time
Go Displacement of Body = Initial Velocity*Time Taken to Travel the Path+(Acceleration of Body*Time Taken to Travel the Path^2)/2
Angular Displacement given Initial Angular Velocity Final Angular Velocity and Time
Go Angular Displacement = ((Initial Angular Velocity+Final Angular Velocity)/2)*Time Taken to Travel the Path
Angular Displacement of Body for given Initial and Final Angular Velocity
Go Angular Displacement = (Final Angular Velocity^2-Initial Angular Velocity^2)/(2*Angular Acceleration)
Final Angular Velocity given Initial Angular Velocity Angular Acceleration and Time
Go Final Angular Velocity = Initial Angular Velocity+Angular Acceleration*Time Taken to Travel the Path
Displacement of Body given Initial Velocity and Final Velocity
Go Displacement of Body = ((Initial Velocity+Final Velocity)/2)*Time Taken to Travel the Path
Angle Traced in Nth Second (Accelerated Rotatory Motion)
Go Angular Displacement = Initial Angular Velocity+((2*Nth Second-1)/2)*Angular Acceleration
Displacement of Body given Initial Velocity Final Velocity and Acceleration
Go Displacement of Body = (Final Velocity^2-Initial Velocity^2)/(2*Acceleration of Body)
Final Velocity of Body
Go Final Velocity = Initial Velocity+Acceleration of Body*Time Taken to Travel the Path
Final Velocity of Freely Falling Body from Height when it Reaches Ground
Go Velocity on Reaching Ground = sqrt(2*Acceleration due to Gravity*Height of Crack)
Distance Travelled in Nth Second (Accelerated Translatory Motion)
Go Distance Traveled = Initial Velocity+((2*Nth Second-1)/2)*Acceleration of Body
Resultant Acceleration
Go Resultant Acceleration = sqrt(Tangential Acceleration^2+Normal Acceleration^2)
Angle of Inclination of Resultant Acceleration with Tangential Acceleration
Go Inclination Angle = atan(Normal Acceleration/Tangential Acceleration)
Tangential Acceleration
Go Tangential Acceleration = Angular Acceleration*Radius of Curvature
Centripetal or Radial Acceleration
Go Angular Acceleration = Angular Velocity^2*Radius of Curvature
Normal Acceleration
Go Normal Acceleration = Angular Velocity^2*Radius of Curvature
Angular Velocity given Tangential Velocity
Go Angular Velocity = Tangential Velocity/Radius of Curvature
Average Velocity of Body given Initial and Final Velocity
Go Average Velocity = (Initial Velocity+Final Velocity)/2

Angle of Inclination of Resultant Acceleration with Tangential Acceleration Formula

Inclination Angle = atan(Normal Acceleration/Tangential Acceleration)
Φ = atan(an/at)

What is resultant acceleration?

Resultant Acceleration is set by the resultant force. When the forces acting on an object do not balance, the resultant force will cause the object to accelerate in the direction of the resultant force. In other words, a resultant force on a body will cause it to change its velocity. This simply means that unbalanced forces will cause acceleration.

What is tangential acceleration?

The concept of tangential acceleration is used to measure the change in the tangential velocity of a point with a specific radius with the change in time. Tangential acceleration is defined as the rate of change of tangential velocity of the matter in the circular path.

How to Calculate Angle of Inclination of Resultant Acceleration with Tangential Acceleration?

Angle of Inclination of Resultant Acceleration with Tangential Acceleration calculator uses Inclination Angle = atan(Normal Acceleration/Tangential Acceleration) to calculate the Inclination Angle, The angle of inclination of resultant acceleration with tangential acceleration is formed by the inclination of one resultant acceleration to tangential acceleration vector; measured in degrees or radians. Inclination Angle is denoted by Φ symbol.

How to calculate Angle of Inclination of Resultant Acceleration with Tangential Acceleration using this online calculator? To use this online calculator for Angle of Inclination of Resultant Acceleration with Tangential Acceleration, enter Normal Acceleration (an) & Tangential Acceleration (at) and hit the calculate button. Here is how the Angle of Inclination of Resultant Acceleration with Tangential Acceleration calculation can be explained with given input values -> 1.566796 = atan(6000/24).

FAQ

What is Angle of Inclination of Resultant Acceleration with Tangential Acceleration?
The angle of inclination of resultant acceleration with tangential acceleration is formed by the inclination of one resultant acceleration to tangential acceleration vector; measured in degrees or radians and is represented as Φ = atan(an/at) or Inclination Angle = atan(Normal Acceleration/Tangential Acceleration). Normal Acceleration is the component of acceleration for a point in curvilinear motion that is directed along the principal normal to the trajectory toward the center of curvature & Tangential acceleration is defined as the rate of change of tangential velocity of the matter in the circular path.
How to calculate Angle of Inclination of Resultant Acceleration with Tangential Acceleration?
The angle of inclination of resultant acceleration with tangential acceleration is formed by the inclination of one resultant acceleration to tangential acceleration vector; measured in degrees or radians is calculated using Inclination Angle = atan(Normal Acceleration/Tangential Acceleration). To calculate Angle of Inclination of Resultant Acceleration with Tangential Acceleration, you need Normal Acceleration (an) & Tangential Acceleration (at). With our tool, you need to enter the respective value for Normal Acceleration & Tangential Acceleration and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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