Concepts and misconceptions - 2

Concepts and misconceptions - 2
Chapter: kinematics

Misconception:

1. A weighing machine measures the weight of a body. ❌

Concept:✔️

The weighing machine measures the reaction between the machine and the The body exerts a force N on the machine and the machine also exerts an equal and opposite force on the body. The weight W of a body of mass m is the gravitational force exerted upon it by body.

N may be same as W. It may also be larger or smaller than W depending upon whether the elevator is accelerating up or down.

W = mg

Misconception

2. Weightlessness means the absence of weight.❌

✔️Weightlessness usually means an absence of reaction between the body and that with which it is in contact.

Misconception:

3. Most of us believe that Newton's first law can be derived from the second law which is absolutely wrong.❌

4. Many of us also have the feeling that action occurs before the reaction. ❌

But actually, both occurs at the same time.✔️

5. Action and reaction act on the same body.❌

Action and reaction always act on two different bodies.✔️

6. Right understanding of Newton's law ✔️

(i) The first law tells us about the natural state of motion of a body, which is motion along a straight line with constant speed.

(ii) The second law tells us that if a body does not follow its natural state of motion then it is under the influences of other bodies, that is, a net unbalanced force must be acting on it.

(iii) The third law tells us about the nature of that force. That is, forces exist in pairs.

7. Misconceptions:

1. The natural state of matter is that of rest.

2. If there is no force, there is no motion.

3. If there is motion, there must be a force.

4. Force acts in the direction of motion.

Since these statements are true in a number of familiar situations, therefore, there is a tendency to believe that they are generally true-in fact, they are wrong.❌

The truth is as follows:
❓❓

1. The natural state of matter is that of motion

2. Gravitational force is acting on a body in rest

3. Freely falling bodies move without external force.

4. Not necessary. Force acts downward on a body moving in an upward direction.

Misconception:

7. When force is parallel to the direction of motion of the body, the work done is minimum.❌

When a force acts parallel to the direction of motion of a body, the work done by the force is given by the formula W = Fd cos θ, where W is the work done, F is the magnitude of the force, d is the displacement of the body, and θ is the angle between the force and the displacement vectors. When the force is parallel to the direction of motion, θ = 0, and cos θ = 1. Therefore, the work done is W = Fd, which is the product of the force and the displacement.

In this case, the work done is not necessarily minimum, but rather it is maximum because the force is acting in the same direction as the displacement. The work done is the product of the magnitude of the force and the distance that the object moves in the direction of the force, and this product is maximized when the force and displacement are parallel.

On the other hand, when the force is perpendicular to the direction of motion, θ = 90°, and cos θ = 0, so the work done is zero. Therefore, the work done is minimum when the force is perpendicular to the direction of motion.

8. An angular velocity of 60 rpm is the same as 2π rad/s.✔️

In general, to convert from revolutions per minute (rpm) to radians per second (rad/s), we can use the following formula:

angular velocity in rad/s = (angular velocity in rpm) x (2π/60)

So for an angular velocity of 60rpm, we have:

angular velocity in rad/s = (60 rpm) x (2π/60) = 2π rad/s

9. One radian means arc length of unit radius is unity.✔️

One radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

Another way to say it is that one radian is the measure of an angle that, when its vertex is at the center of a circle, the arc it cuts off on the circumference of the circle has a length equal to the radius of the circle.

This means that the length of the arc is equal to the radius, so if we take a circle with a radius of 1 unit, then one radian is the angle that cuts off an arc of length 1 unit.

Misconception

10. When an object is moving in a circle, the angle b/w linear velocity and position vector is 90°

No, that's not correct. When an object is moving in a circle, the angle between the linear velocity and the position vector is not always 90°.

In fact, the angle between the linear velocity and the position vector changes continuously as the object moves around the circle. At any given point on the circle, the position vector points from the center of the circle to the object, while the linear velocity vector points tangent to the circle at that point. The angle between these two vectors at that point is the angle between a tangent line and a radius line, which is not always 90°.

However, it is true that the position vector, the linear velocity vector, and the acceleration vector of an object moving in a circle are all mutually perpendicular at any instant when the object is at the maximum displacement from the center of the circle (i.e., at the top or bottom of the circle, if the circle is oriented vertically).

This is because the acceleration vector is always directed towards the center of the circle, while the position vector and the linear velocity vector are both perpendicular to the acceleration vector.

Misconception

11. The value of angular momentum is maximum when the angle is 90°.

No, that's not correct. The value of angular momentum is not necessarily maximum when the angle is 90°.

Angular momentum is a vector quantity that describes the amount of rotational motion an object has around a particular axis. It depends on the object's moment of inertia, which is a measure of its resistance to rotational motion, as well as its angular velocity. The formula for angular momentum is L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

The direction of the angular momentum vector is perpendicular to both the moment of inertia vector and the angular velocity vector. The magnitude of the angular momentum vector is equal to the product of the moment of inertia and the angular velocity.

The angle between the moment of inertia vector and the angular velocity vector can vary, depending on the geometry of the object and the direction of its angular velocity. Therefore, the value of angular momentum can have different magnitudes at different angles between the moment of inertia and the angular velocity vectors. It is not necessarily maximum when the angle is 90°.

However, when an object is rotating about a fixed axis, the direction of the angular momentum vector is always along the axis of rotation. The magnitude of the angular momentum can vary depending on the speed of rotation and the moment of inertia of the object, but the direction is always along the axis of rotation.

Misconception

12. Vertical velocity vs time graph for a projectile motion varies linearly.

That is not correct.

In projectile motion, the vertical velocity of the projectile changes due to the effect of gravity. Gravity causes the projectile to accelerate downward with a constant acceleration of 9.8 m/s^2 (assuming negligible air resistance).

Therefore, the vertical velocity vs time graph for a projectile motion does not vary linearly, but rather as a parabolic curve. Initially, the vertical velocity is zero at the highest point of the motion, then it increases in the negative direction (i.e. downward) due to gravity, until it reaches a maximum negative velocity at the bottom of the trajectory. It then slows down and eventually reaches zero again when the projectile reaches the same height from which it was launched. The vertical velocity vs time graph for a projectile motion looks like a symmetric parabolic curve, with the maximum height corresponding to the vertex of the parabola.