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Mechanics (Essentials) - Class 11th
Course: Mechanics (Essentials) - Class 11th > Unit 12
Lesson 1: How do spinning wheels and moving cars connect? Uncovering the link between angular and linear motion!Introduction to rotational motion review
Overview of key terms, equations, and skills for rotational motion, including the difference between angular and tangential acceleration.
Key terms
| Term (symbol) | Meaning |
|---|---|
| Axis of rotation | The imaginary or actual axis around which an object may rotate. |
| Average angular acceleration (alpha) | Measure of how angular velocity changes over time. The rotational analogue of linear acceleration. A vector quantity with counterclockwise defined as the positive direction. SI units of start fraction, start text, r, a, d, i, a, n, s, end text, divided by, start text, s, end text, squared, end fraction. |
| Tangential acceleration (a, start subscript, t, end subscript) | Linear acceleration of a rotating object that is perpendicular to its radial acceleration. SI units of start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction. |
Equations
| Equation | Symbols | Meaning in words |
|---|---|---|
| v, equals, omega, r | v is linear speed, omega is angular speed, and r is radius | The linear speed is proportional to the angular speed and the radius. |
| alpha, equals, start fraction, delta, omega, divided by, delta, t, end fraction | alpha is average angular acceleration, delta, omega is change in angular velocity, and delta, t is change in time | The average angular acceleration is the change in angular velocity divided by time. |
| a, start subscript, t, end subscript, equals, alpha, r | a, start subscript, t, end subscript is tangential acceleration | The tangential acceleration is proportional to the angular acceleration and the radius. |
Common mistakes and misconceptions
- People sometimes mix up angular and tangential (or linear) acceleration. Angular acceleration is the change in angular velocity divided by time, while tangential acceleration is the change in linear velocity divided by time.
- People sometimes forget that angular acceleration does not change with radius, but tangential acceleration does. For example, for a rotating wheel that is speeding up, a point on the outside covers more distance in the same amount of time as a point closer to the center. It has a much larger tangential acceleration than the portion closer to the axis of rotation. However, the angular acceleration of every part of the wheel is the same because the entire object moves as a rigid body through the same angle in the same amount of time.
Learn more
For deeper explanations of angular quantities, see our videos angular motion variables and relating angular and regular motion variables
To check your understanding and work toward mastering these concepts, check out the exercises in this tutorial.
Want to join the conversation?
Are rotational motion and angular motion are same thing ? Or are they two different things ?(1 vote)- I think they're the same thing. The actual name is angular velocity and angular acceleration.(5 votes)
Why do we need to take the reciprocal of angular acceleration after we use a = R alpha?(2 votes)- why angular frequency remains constant whereas time period is not constant(1 vote)
Think of angular frequency as the number of times a point on the circle completes a revolution in a given amount of time (for SI units, it would be in one second). Though time period for which it is measured may not be constant, the point will still go the same number of revolutions in a single second regardless of whether you are measuring for one second or 2 seconds or even 5 seconds.(1 vote)
- Is rotational motion dimensionless(1 vote)
- How do you figure out which type of acceleration the problem id giving to you if it does not have units. Ex) A n object with a diameter of 36m is turning about an axis at a constant rate. How would I know that thats angular acceleration?(1 vote)
The author of this article made a mistake, v should be defined as speed of object.(0 votes)- v (aka speed) is also known as the linear velocity (or tangential velocity), as it is the instantaneous velocity of the object at that point in the rotational motion(7 votes)
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what is the basics of rotational motion in rotationa(0 votes)