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Tangential Acceleration Formula can be understood by the following lines. In a circular motion, particles can accelerate, decelerate, or move at a constant velocity. When a particle is in a circular motion, there is always an acceleration towards the centre called the centripetal acceleration (even if it is moving at a constant velocity).
However, when the velocity changes, the tangential acceleration in the direction or opposite direction works the same as the tangential acceleration of the velocity. For example, tangential and centripetal acceleration occur after a car travels on a curve on the road.
| Table of Content |
Keyterms: Acceleration, Circular motion, Velocity, Velocity vector, Force, Magnitude, Radius
Tangential Acceleration
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In a uniform circular motion, the net force acting on the object is perpendicular to the motion of the object. Therefore, the direction changes continuously, but the magnitude of the velocity remains constant. Hence, the object accelerates in the direction of the circular orbit’s centre. But what if the net force acting on the object is not vertical? In this case, there is a two-component force vector pointing vertically and parallel to the velocity vector.
The vertical force component moves the object along a circular path while creating centripetal acceleration, and the parallel force component accelerates the object along the tangential line while creating tangential acceleration. Therefore, the object experiences a non-uniform circular motion because both the direction and magnitude of the object's velocity change.
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Tangential Acceleration Formula
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The formula for calculating tangential acceleration is as follows:
Tangential Acceleration= (rotation’s radius) × (angular acceleration)
Which can also be written as at=v/t
Tangential Acceleration Formula In Terms Of Distance
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The tangential acceleration formula in the terms of distance is written as follows:
at= d2s/dt2 or also as at=v. dv/ds
The notations used in the above-mentioned formulae are as follows:
- Δv is the change in the angular velocity
- v is the linear velocity
- Δt is the change in time
- at is the tangential acceleration
- t is the time taken
- s is the distance covered
The unit assigned to these quantities obtained from using the formulae mentioned above is m/s2.
Also Read: Motion in a Straight Line
Linear Acceleration Formula
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Linear acceleration is defined as the uniform acceleration caused by the linear movement of an object. There are three important equations for linear acceleration, depending on parameters such as start and end speeds, displacement, time, and acceleration.
The following table describes the three equations used in linear acceleration.
| The First Equation of Motion | v = u = at |
| The Second Equation of Motion | s = ut + 12at2 |
| The Third Equation of Motion | v2 = u2 + 2as |
The following Notations were Used In This Formula:
- a is the acceleration
- u is the initial velocity
- t is the time taken
- s is the acceleration
- v is the final velocity
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| Projectile Motion Formula | Resultant Vector Formula | Relation between Torque and speed |
| Horizontal Motion | Velocity Vectors | Trajectory Formula |
Things to Remember
- In a uniform circular motion, the net force acting on the object is perpendicular to the motion of the object. Therefore, the direction changes continuously, but the magnitude of the velocity remains constant. Hence, the object accelerates in the direction of the circular orbit’s centre.
- The formula for calculating tangential acceleration is as follows: Tangential Acceleration= (rotation’s radius) × (angular acceleration) Which can also be written as at=v/t
- Linear Acceleration is defined as the uniform acceleration caused by the linear movement of an object. There are three important equations for linear acceleration, depending on parameters such as start and end speeds, displacement, time, and acceleration.
- The tangential acceleration formula in the terms of distance is written as follows: at = d2s/dt2 or also as at=v. dv/ds
Previous Year Questions
- The acceleration of moving the body from rest is 2 (t - 1). Then, the velocity at 5 s will be…[RPET 2002]
- A particle is projected with a velocity of 100 at 30. The time of the flight is...[COMEDK UGET 2006]
- The range of a particle projected at an angle of 15? with the horizontal is 1.5 km. Its range when projected with the same velocity at an angle of 45? with the horizontal is...[COMEDK UGET 2008]
- The width of the river is 1 km. The velocity of the boat is 5 km/hr. The boat covered the width of the river in the shortest time 15 min. Then the velocity of the river stream is…[NEET 1998]
- When milk is churned, the cream gets separated due to...[NEET 1991]
- Which of the following is not a vector quantity?...[KCET 2014]
- The angle between velocity and acceleration of a particle describing uniform circular motion is...[KCET 2017]
- A stone of mass 1 kg tied to the end of a string of length 1 m, is whirled in a horizontal circle, with a uniform angular velocity of 2 radian/sec. The tension of the string is (N)...[KCET 1998]
- Which of the following statements is true?...[JKCET 2006]
- A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5m/s. What is the height of the plane of the circle from a vertex of the funnel?...[JKCET 2005]
Sample Questions
Ques: Why study rotational motion, and what specifies centripetal acceleration? (4 marks)
Ans: Rotational mechanics is one of the key topics in mechanics that requires great imagination and intuition. This helps us understand the mechanism behind the rotational motion we are studying in electric motors and generators.
In rotational motion, tangential acceleration is a measure of the rate of change in tangential velocity. It always works orthogonally to the centripetal acceleration of the rotating object. This is equal to the product of the angular acceleration α and the radius of gyration. Tangent acceleration = radius of a rotation its angular acceleration.
It is always measured in radians/second squared. The formula is [T-2].
Ques: Why study tangential acceleration? What is a tangential velocity vector? (4 marks)
Ans: When an object makes a circular motion, it experiences not only afferent but also tangential acceleration. The components of the acceleration of curved motion are the radial and tangential accelerations. The tangential component is generated by changes in running speed. Points in the direction of the velocity vector along the curve. Also in the opposite direction.
The tangential velocity acts in the direction of the tangent at the point of circular motion. After that, it always acts in the direction perpendicular to the centripetal acceleration of the rotating object. This is always equal to the product of the angular bend radius of gyration.
Ques: At speeds of 20 m / s to 80 m / s in 30 seconds, the object accelerates uniformly in a circular orbit. Find the tangential acceleration. (3 marks)
Ans: Given parameters:
vi = 20 m / s
vf = 80 m / s
dv = vf-vi = 80-20 = 60 m / s
dt = tf-ti = 30-0 = 30 seconds
The formula for tangential acceleration is:
af = dv / dt
at = 60/30
at = 2 m/s2
Ques: In what direction does the tangential acceleration act? (2 marks)
Ans: The tangential acceleration acts in the direction of the tangent at the point of circular motion. Its direction is always perpendicular to the centripetal acceleration of the rotating object.
Ques: What kind of force does tangential acceleration cause? (2 marks)
Ans: The tangential force component causes tangential acceleration, accelerating the object along the tangential line. As the direction and magnitude of the object's velocity change, the object experiences a non-uniform circular motion.
Ques: Give examples of afferent and tangential acceleration. (3 marks)
Ans: Suppose you have a rope and its ends are fixed to a stone. If you start spinning here, you will notice that you need to apply two forces at the same time. One pulls the wire inward and the other pulls the wire laterally or tangentially. Both forces generate their respective accelerations. Those facing inward produce an afferent or radial b, and those facing sideways produce tangential acceleration.
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