1.6 - Tangential Acceleration

Phreestyle Physics
5 Sept 201406:41
EducationalLearning
32 Likes 10 Comments

TLDRThis educational video script delves into the concept of tangential acceleration in non-uniform circular motion. Unlike uniform circular motion, where speed remains constant, non-uniform circular motion involves changing speeds, thus introducing tangential acceleration. The script explains that acceleration has two components: radial and tangential. Radial acceleration is associated with changes in direction towards or away from the center, while tangential acceleration affects the speed along the circle's tangent. The instructor uses kinematic equations to illustrate how tangential acceleration influences arc length, and emphasizes the distinction between radial and tangential accelerations, clarifying that kinematic principles apply to circular motion only when considering motion along the circle's path.

Takeaways
  • 📚 The lecture discusses tangential acceleration in the context of circular motion, differentiating it from uniform circular motion where there is no change in speed.
  • 🔄 Even though an object in uniform circular motion is accelerating towards the center, it does not change speed, but when the speed changes, there is an additional component of acceleration.
  • 👉 The two components of acceleration in circular motion are radial and tangential; radial is directed towards or away from the center, while tangential is perpendicular to the radius.
  • 🎯 The direction of tangential acceleration is the same as the direction of velocity when the object is speeding up tangentially, which is away from the center at the top of the circle.
  • 📉 The formula for the arc length (s) in circular motion is given as \( s_{final} = s_{naught} + v_{naught} \cdot T + \frac{1}{2} a_{tangent} \cdot T^2 \), where \( T \) stands for tangential time.
  • ❗ It's important to note that kinematic equations do not apply to centripetal acceleration in the same way they do for tangential acceleration due to the nature of circular motion.
  • 🔧 When an object is speeding up in circular motion, it experiences radial acceleration, which changes the magnitude of its velocity, not just its direction.
  • 🌀 The magnitude of centripetal acceleration is still given by \( v^2 / R \), where \( R \) is the radius of the circle, and \( v \) is the velocity at any given instant.
  • 🧭 The actual direction of acceleration in circular motion is the vector sum of the radial and tangential components, which is not always directly towards or away from the center.
  • 📚 The lecture emphasizes the importance of understanding the different components of acceleration in circular motion and how they affect the motion of an object.
Q & A

  • What is tangential acceleration?

    -Tangential acceleration is the rate of change of tangential velocity, which occurs when an object is changing its speed while moving in a circular path.

  • Is there tangential acceleration in uniform circular motion?

    -No, in uniform circular motion, there is no tangential acceleration because the speed of the object is constant, although there is still centripetal acceleration towards the center of the circle.

  • What are the two components of acceleration when an object is moving in a circle?

    -The two components of acceleration when an object is moving in a circle are radial acceleration (towards or away from the center) and tangential acceleration (perpendicular to the radius).

  • What is the direction of the tangential acceleration when an object is speeding up in a circular path?

    -The direction of the tangential acceleration is the same as the direction of the tangential velocity, which is perpendicular to the radius of the circle.

  • How is arc length related to tangential acceleration?

    -Arc length (s) can be related to tangential acceleration through the kinematic equation: s_final = s_initial + v_initial * t + 0.5 * a_tangential * t^2, where t is time.

  • Can kinematic equations be applied to centripetal acceleration?

    -No, kinematic equations cannot be applied to centripetal acceleration because the displacement towards the center in circular motion is not a straight line, making it unsuitable for kinematic analysis.

  • What is the relationship between centripetal acceleration and the radius of the circle?

    -The centripetal acceleration (a_c) is equal to the square of the velocity (v^2) divided by the radius (R) of the circle, expressed as a_c = v^2 / R.

  • Does the magnitude of centripetal acceleration change when an object is speeding up in a circular path?

    -Yes, the magnitude of centripetal acceleration increases when an object is speeding up in a circular path because it is directly proportional to the square of the velocity.

  • What is the actual direction of acceleration when an object has both radial and tangential components?

    -The actual direction of acceleration is the vector sum of the radial and tangential components, which is not along the radius but at an angle to it, pointing towards the center and in the direction of tangential velocity.

  • How should vectors be added when determining the net acceleration?

    -Vectors should be added by aligning them tail to head (or head to tail) and summing the components along each axis to determine the net acceleration.

Outlines
00:00
🔄 Tangential and Radial Acceleration in Circular Motion

This paragraph discusses the concept of tangential and radial acceleration in non-uniform circular motion. It explains that while uniform circular motion involves constant speed and only centripetal acceleration towards the center, non-uniform circular motion includes a tangential acceleration component as well. The speaker uses a demonstration to illustrate the direction of tangential acceleration, which is perpendicular to the radius and points in the direction of increasing speed. The kinematic equation for arc length in circular motion is introduced, highlighting the role of tangential acceleration in determining the distance traveled around the circle. The paragraph also clarifies that kinematic principles do not apply to centripetal acceleration, which is always directed towards the center of the circle.

05:00
📉 Understanding the Components of Acceleration in Circular Motion

The second paragraph delves deeper into the components of acceleration during circular motion. It emphasizes that even when an object is speeding up in a circular path, there is still a centripetal component of acceleration that is equal to the square of the velocity divided by the radius (V^2/R) at any given instant. The paragraph clarifies a common misconception regarding the direction of the total acceleration vector, which is the vector sum of the centripetal and tangential components. The speaker instructs the audience to visualize and point towards the actual direction of acceleration, which is not solely towards the center but also includes the tangential component. The importance of correctly adding vectors to find the net acceleration is also highlighted, using a visual method to demonstrate how the centripetal and tangential accelerations combine.

Mindmap
Keywords
💡Tangential Acceleration
Tangential acceleration refers to the rate of change of tangential velocity, which is the component of velocity that is parallel to the path of an object moving along a curve. In the context of the video, the instructor is discussing how an object undergoing circular motion can have a tangential acceleration if its speed is changing, even though it is still accelerating towards the center due to centripetal force. The script mentions that the object is 'accelerating tangentially' when it is speeding up in the direction of its velocity.
💡Uniform Circular Motion
Uniform circular motion is a type of motion where an object moves in a circular path at a constant speed. The video script contrasts this with a scenario where the speed is changing, indicating that the motion is no longer uniform. The instructor clarifies that in uniform circular motion, there is no tangential acceleration, but there is still centripetal acceleration towards the center of the circle.
💡Radial Acceleration
Radial acceleration, also known as centripetal acceleration, is the acceleration directed towards the center of the circle in circular motion. The script explains that while an object in uniform circular motion has a constant radial acceleration, when the speed changes, there is an additional component of acceleration, the tangential acceleration, making the radial acceleration non-constant.
💡Tangential Component
The tangential component refers to the part of the motion or force that is parallel to the direction of motion. The video script uses the term to describe the tangential acceleration, which is a component of the total acceleration when an object's speed changes while moving in a circle. It is distinguished from the radial component, which is directed towards the center of the circle.
💡Arc Length
Arc length, denoted by 's' in the script, is the distance along the circular path that an object has traveled during its motion. The instructor uses the term in the kinematic equation for circular motion, where the final arc length is the sum of the initial arc length, the product of initial tangential velocity and time, and half the product of tangential acceleration and the square of time.
💡Kinematics
Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. In the video, the instructor explains that kinematic equations can be applied to the tangential component of motion in a circle, allowing for calculations of arc length and velocity, but not for the radial component, which is related to centripetal force.
💡Centripetal Acceleration
Centripetal acceleration is the acceleration that keeps an object moving in a circular path, always directed towards the center of the circle. The script emphasizes that even when an object has tangential acceleration, the centripetal acceleration still exists and is given by the formula V^2/R, where V is the velocity and R is the radius of the circle.
💡Angular Acceleration
Angular acceleration is the rate of change of angular velocity. The video script introduces the concept by discussing how the magnitude of centripetal acceleration changes as the object's speed increases, indicating that there is an angular acceleration involved in the motion.
💡Vector Addition
Vector addition is the process of combining two or more vectors to find the resultant vector. In the context of the video, the instructor demonstrates vector addition to find the net acceleration of an object in circular motion, which is the sum of the centripetal and tangential accelerations. The script specifies the correct method of adding vectors by connecting the tail of one vector to the head of another.
💡Net Acceleration
Net acceleration is the vector sum of all the individual accelerations acting on an object. The script uses the term to describe the total acceleration experienced by an object in circular motion when both tangential and centripetal accelerations are considered. The net acceleration is the actual direction of acceleration that the object feels as it moves in the circle.
Highlights

Introduction to tangential acceleration and its distinction from uniform circular motion.

Uniform circular motion involves acceleration towards the center but no change in speed.

Exploration of non-uniform circular motion with changing speed and its implications.

Introduction of two components of acceleration in circular motion: radial and tangential.

Explanation of radial direction as being parallel to the radius.

Clarification of tangential direction as being perpendicular to the radius.

Demonstration of the direction of tangential acceleration during circular motion.

Illustration of the object's velocity and acceleration at the top of the circular path.

Kinematic equation for arc length in circular motion involving tangential velocity and acceleration.

Differentiation between kinematic equations for circular motion and centripetal acceleration.

Discussion on radial acceleration and its relation to the changing speed in circular motion.

Explanation of centripetal acceleration's magnitude and its relation to velocity and radius.

Clarification that centripetal acceleration is always directed towards the center of the circle.

Vector addition of radial and tangential acceleration to determine the net acceleration.

Visual representation of the actual direction of acceleration in non-uniform circular motion.

Emphasis on the importance of understanding the components of acceleration in circular motion.

Transcripts

Browse More Related Video

Circular Motion: Acceleration (Angular, Tangential, Centripetal)

AP Physics C: Rotational Kinematics Review (Mechanics)

Uniform Circular Motion and Centripetal Force

Rotational Motion: An Explanation, Angular Displacement, Velocity and Acceleration

Relating angular and regular motion variables | Physics | Khan Academy

Uniform Circular Motion - IB Physics

Rate This

5.0 / 5 (0 votes)

Thanks for rating:

Related Tags
Circular MotionTangential AccelerationCentripetal AccelerationPhysics ConceptsKinematicsUniform MotionRadial DirectionTangential DirectionAcceleration VectorsEducational Content