For very small angles, you can approximate values for the sine, cosine, or tangent. This is useful when calculating the fringe separations in interference patterns. When θ is measured in radians, a small angle segment approximates to s/r where s is the arc length and r is the radius. In other words, for a small […]

# Rotational Motion_21

## Rolling Motion (or plane motion) & its types

The motion of a rigid body undergoing rotation about an axis, with the axis of rotation having a translational motion, is called rolling motion or plane motion. Thus rolling motion is a combination of translational and rotational motion. Examples: A spinning ball thrown in the air, wheels of vehicles moving on the road, etc are […]

## Pure Rotational Motion of rigid bodies

In this post, we will discuss the Pure Rotational Motion of rigid bodies, and also analyze an example with a supporting diagram. Then we will discuss Pure translational motion with a diagram. Once we do these, we will quickly compare Pure Rotational Motion and Pure translational motion. Pure Rotational Motion of rigid bodies – characteristics […]

## Relating the linear and angular variables

We often need to relate the linear variables s, v, and a for a particular point in a rotating body to the angular variables θ, ω, and α for that body. The two sets of variables are related by r, the perpendicular distance of the point from the rotation axis. This perpendicular distance is the […]

## Can an object moving in a straight line, have angular momentum?

An object moving in a straight line (having linear momentum) can have angular momentum. For example, let’s say we throw a ball at one end of a stick (see Figure 1). The stick can pivot around point O. When the ball hits the stick, the stick rotates. If the system of the ball and stick has […]

## Rolling along an inclined plane or ramp – a study of the combined rotation and translation of a cylinder

The topic of this post is Rolling along an inclined plane or ramp and here we will do a will study of the combined rotation and translation of a cylinder along a ramp. a study of the combined rotation and translation of a cylinder | Rolling along an inclined plane or ramp When a cylinder […]

## Numerical problem on Rotational Kinetic Energy

In this post, we will review the formula of Rotational Kinetic Energy and then solve numerical problems based on Rotational Kinetic Energy. Rotational Kinetic Energy formula from the linear kinetic energy formula The equation for linear kinetic energy = KEL = (1/2) m v2 Let’s Convert that equation to its angular analog: KE = (1/2) […]

## Numerical problem on rotational work | Numerical on work done by the torque

In this post, we will find the equation of the work done by Torque. (In other words, we will work with the equation of rotational work.) Then we solve a few numerical problems using this formula of rotational work. Equation of the work done by Torque | equation of rotational work Here we will find […]

## Moments of Inertia – formulas & sample numerical

In this post, we will focus on the formulas of the moment of inertia and also will solve a few interesting sample numerical problems using the moment of inertia formulas. Moments of Inertia – concepts & definition The torque equation gives us: τ =mr2α . This is an important result because it relates to torque […]

## Angular Momentum, moment of inertia & Rotational motion

In this post, we will discuss a couple of interesting questions related to Angular Momentum, Torque, moment of inertia & Rotational motion. How does angular momentum work in rotational motion? The angular momentum of a rotating object is equal to the product of its moment of inertia and its angular velocity. If there is no […]

## How to solve leaning ladder equilibrium numerical?

In this post, we will solve a numerical problem based on the equilibrium of a leaning ladder. To do this you need to first understand the conditions of equilibrium. If you require some revision then you can quickly go through our physics tutorial on the equilibrium conditions first, before attempting this numerical. Anyways, let’s begin […]

## Derivation of the total Kinetic energy Equation for Combined Translation and Rotation | Rotation of a rigid body about a moving axis

Before going for the Derivation of the equation of total Kinetic energy of a body under combined translation and rotation, let’s do some analysis of the dynamics of Rigid-Body Rotation About a Moving Axis to some cases in which the axis of rotation moves. When that happens, the motion of the body is a combination […]

## Rotational Kinematics Numerical Problems and solutions

This post is all about Rotational Kinematics Numerical Problems and solutions. We will use the following four rotational kinematic equations (presented together with their translational counterparts) to solve the numerical problems. Rotational kinematic equations | equations used to solve rotational motion numerical In these equations, the subscript 0 denotes initial values (ω0 and vo are initial values). […]

## Derive the Rotational Kinetic Energy Equation | Derivation of Rotational KE formula

Here we will derive the Rotational Kinetic Energy Equation in a few easy steps. This equation expresses the kinetic energy of a rotating object just because of its rotational motion. So, let’s begin the derivation. How to derive the Rotational Kinetic Energy Equation | Rotational KE formula derivation To derive the rotational kinetic energy equation, […]

## How is the Stability of floating bodies maintained? | (equilibrium of a floating ship)

How is the stability of floating bodies maintained? The stability of stationary floating bodies is maintained when the conditions of floating are satisfied. But when a floating body like a ship is tilted then it can get back its stability (through stable equilibrium) if the couple created by its downward weight and the upthrust working […]

## Numerical Problems on Rolling motion, Torque, and Angular Momentum

Numerical Problems on Rolling motion, Torque, and Angular Momentum (worksheet with medium & Hard problems)

## Moments of Inertia of various bodies – quick reckoner chitsheet with diagram and equations

Here is a quick reckoner for the equations of moments of inertia of various bodies of various shapes (in diagram form) The diagram (figure 1) shows the Moment of Inertia formulas of the following:(a) Slender rod with the axis through center (2) Slender rod axis through one end (3) rectangular plate axis through center (4) […]

## What is the principle of moments and how to use it to solve numerical problems?

Here we will state the principle of moments first and then will see how to use it to solve numerical physics problems related to equilibrium. What is the principle of moments? The Principle of Moments states that the rotational equilibrium of a body is possible only when the sum of clockwise moments is equal to […]

## How to convert between degrees and radians -degree and radian conversion formulas

Angular displacement is often expressed in one of three units. The first is the degree, and it is well known that there are 360 degrees in a circle. The second unit is the revolution (rev), one revolution representing one complete turn of 360 degrees. The most important unit from a scientific viewpoint, however, is the […]

## What is the difference between Circular motion and rotational motion – are they the same?

Rotational motion is a type of circular motion. In other words, all circular motions can’t be called rotational motion, but all rotational motions are certainly circular motions. When an object turns, it’s in a circular motion irrespective of the position of its axis. But for a rotational motion, the axis has to be located within the body of the object.

## Moment of Couple & its formula

Moment of Couple – this term in physics is based on an understanding of 2 concepts, the first one is ‘moment’ and the second one is ‘couple’. The moment in physics denotes the turning effect. A couple in physics is discussed in our post on Couple – you can read it here. Moment of Couple […]

## Couple in physics – class 10 notes

A couple in physics – this is our topic in this post. Now let’s first define a couple in Physics. Two equal, opposite, parallel forces, not acting along the same line, form a couple. A couple is always needed to produce rotation. Two forces F and −F, having the same magnitude, parallel lines of action, […]

## What is the moment of force and how to measure it? (class 10)

Today’s topic is about Moment of Force – we will discuss it in detail. When a force is applied on a suitable point of a pivoted body and a turning effect of the body is witnessed then we can say that a moment of force is produced. In other words, the turning effect of a […]

## Law of Conservation of Angular Momentum – statement and derivation

In this post, we will study the Law of Conservation of Angular Momentum with its statement and derivation. State the Law of Conservation of Angular Momentum The Law of Conservation of Angular Momentum states that angular momentum remains constant if the net external torque applied on a system is zero. So, when net external torque […]

## Torque Physics with definition and Examples

Let’s start with Torque physics and the Definition of Torque is the first point of our discussion here. Torque is the Moment of Force (Rotational domain equivalent of Force). It is the determining factor of how effectively a force can twist or turn something. It is expressed as the cross product of force and the […]

## Torque Formula – What is Torque, Calculation, Derivation

Torque formula can be framed considering Torque as the Moment of Force. It is the cross product of Lever Arm Length (r) and the Force applied (F).

T = r x F = r F Sin θ

## Angular Momentum

When an object moves with an angular speed ω along the circumference of a circular path of radius r, then we say that it has angular momentum. Angular momentum is the rotational equivalent of linear momentum and is defined as the moment of Linear momentum. It depends on 2 quantities, one is rotational inertia or […]