Exams Prep Master
Rotational motion and translational motion are similar to each other. Rotational motion terms like angular acceleration and angular velocity are analogous to term velocity and acceleration in translational motion. Considering this, we can say that the rotation of a body about a fixed axis is analogous to the linear motion of a body in translational motion. Rational motion is defined as the motion of a body in such a way that all of its particles move in circles about an axis with a common angular velocity. On the other hand, in transitional motion the moving body moves uniformly in the same line or direction. In this article, we will explain the kinematics of rotational motion around a fixed axis.
| Table of Contents |
Key Takeaways: Rotational motion, Translational Motion, Angular Velocity, Acceleration
Angular Acceleration
[Click Here for Sample Questions]
Angular acceleration is defined as the rate of change in angular velocity. It is written as:
α = dω/dt ( rad/sec²)
Suppose P as a rotating object. The object rotates at the fixed point. The angular displacement of P is θ. Thus in time t=0. The angular displacement of P is 0. Therefore, we can say that in time (t), its angular displacement will be equal to θ.
Angular Velocity
[Click Here for Sample Questions]
The rate of change of angular displacement is known as angular velocity. The formula of angular velocity is
ω = dθ/dt
The rotational motion here is fixed, so there is no change in angular velocity. Angular acceleration is α = dωdt. So the kinematics equations of linear motion with uniform acceleration is,
v = v0+ at
x = x0 + v0t + 12 at²
v² = v02+ 2ax
Where x0 is the initial displacement and v0 is the initial velocity of the particle. Here initial means t = 0. Now, this equation corresponds to the kinematics equation of the rotational motion.
Kinematics Equations for Rotational Motion with Uniform Angular Acceleration
[Click Here for Sample Questions]
The equations analogous to these for rotational motion can be given as:
Where Ɵ0 is the initial angular displacement, is the initial angular velocity, α is the angular acceleration, ω is the angular velocity at any instant t.
Rotational Kinematics Formula
Ɵ - Ɵ0 = (ω0z + ωz/ 2)t
- Ɵ0 = the initial angular displacement around the z-axis in radians
- Ɵ = the final angular displacement around the z-axis in radians
- ω0z = the initial angular velocity around the z-axis s-1
- ωz = the final angular velocity around the z-axis s-1
- t = the time in s
Things to Remember
- The kinematics of rotational motion defines the relationships between the angular velocity, angular acceleration, angle of rotation and time.
- In rotational motion the body moves in circular motion about a fixed axis with a common angular velocity and angular acceleration.
- In translational motion, the body moves in a straight line or direction. In translational motion there is no change in the orientation of the object.
Sample Questions
Ques. Suppose a wheel rotating with uniform angular acceleration covers 50 rev in the first five seconds after the start. Find the value of x, If the angular acceleration at the end of five seconds is x π rad/s². (2 marks)
1) 10
2) 4
3) 8
4) 6
Ans. 8
θ = 1/2 αt²
α = 2θ/t² = 2(50)(2π)/5² = 8π rad/s² = 25.14 rad/s²
comparing with α, x = 8 rad/s²
Ques. What is the definition of rotational motion? (2 marks)
Ans. Rotational motion is defined as the motion of a rigid body in a way that all particles move in circles about an axis with a common angular velocity.
Ques. What is translational motion? (1 marks)
Ans. Translational motion is defined as the motion in which a body moves uniformly in one direction.
Ques. State a few examples of rotational motion in our day to day life? (2 marks)
Ans. Some examples of rational motions are mentioned below:
- The rotation of a spinning top
- The rotation of earth
- Movement of ceiling fan
- Rotation of windmill
Ques. How can we relate rotational kinematics and translational kinematics quantities? (3 marks)
Ans. The translational kinematic quantities like displacement, velocity, and acceleration can be related to rotational motion quantities angular displacement, angular velocity, and angular acceleration respectively as they have a direct analogy with each other.
The three equation of motion were,
v = v0 + at is analog to ω = ω0 + αt
x = x0 + v0t + (1/2) at² is analog to θ = θ0+ ω0t + (1/2) αt²
v² = v02 + 2ax is analog to ω² = ω0² + 2α (θ – θ0)
Ques. State the difference between circular motion and rotational motion? (3 marks)
Ans. The main difference between them is that circular motion is just a special case of rotational motion. In circular motion the distance between the body's centre of mass and the axis of rotation always remains fixed. On the other hand, rotational motion is based around the idea of rotation of a body about its centre of mass. Therefore, circular motion is a special type of rotational motion.
Ques. Write a few examples of translational motion? (2 marks)
Ans. Some of the examples of translational motion are:
- A car moving in straight line
- A bullet fired from gun
Comments