Force, Inertia and the First Law

Transcript

0:00Introduction

Hello everyone! Okay, picture this. You are standing in a bus moving at a steady speed. Suddenly, the driver brakes, and you fall forward. Now tell me, who pushed you? Nobody, right? And when the bus starts suddenly, you fall backward. Again, nobody pushed you! So what moved you? Newton's first law answers both. And look, this lesson is the base of the whole unit on laws of motion; JEE questions on it come up often. So, let's begin.

0:33Force and inertia

So, first things first. Force is simply a push or a pull. Nothing more complicated than that, okay? And here is what a force can do. It can change a body's state of rest, or of uniform motion. Uniform motion means the same speed in the same direction. Clear? Now, the opposite case. Suppose nothing pushes or pulls a body at all. What will that body do? Very good! It just keeps doing what it was doing. At rest, it stays at rest. Moving uniformly in a straight line, it keeps moving that way. This tendency is called inertia. Bodies are lazy; they do not like to change their state. Right? And the measure of inertia is the mass of the body. More mass, more inertia. Got it?

1:21Back to the bus

Now, back to our bus. Your feet are on the floor, so friction with the floor carries them along with the bus. But your upper body only has its inertia. So, the bus brakes suddenly, and your feet slow down with it. What does your upper body do? Yes, exactly! It keeps moving forward, so you fall forward. The double arrow on screen means, so. This is called inertia of motion. Nobody pushed you; your body simply kept going! Now the bus starts suddenly. The feet are carried forward, but the upper body tends to stay at rest, so you fall backward. This is inertia of rest. Puzzle solved! With me?

2:04Newton's first law

So now, Newton's first law. It says, a body stays at rest, or keeps moving with constant velocity, unless a net external force acts on it. Net means all the forces added together, and external means coming from outside the body. Notice, this is exactly the inertia we just saw. Okay? Now in symbols. The big Greek letter sigma means sum, and F with an arrow on top is a force vector. So sigma F vector is the net force. It equals the zero vector, the zero with an arrow, if and only if v vector, the velocity, is constant. The double-headed arrow means, if and only if: it works both ways. Right?

2:47Trap: a moving car with zero net force?

Now, a trap that catches many students. Take a car moving at a steady ninety kilometres per hour, on a straight, level road. The k m and the h to the minus one on screen mean kilometres per hour, okay? Its engine is running. So, is the net force on this car zero? If you said no, you just fell into the trap! The engine's forward push reaches the car through the road, as friction on the tyres. And this push is balanced by air drag, the air pushing back on the car. So the net force is zero, and yet the car keeps moving at ninety. Exactly what the first law says: zero net force, constant velocity. Clear? So write this down. Zero net force means zero acceleration, not zero velocity. The body can be at rest, or moving steadily; both are fine. Got it?

3:41Inertial frames

Now, one condition. We always describe motion from some frame of reference, like the ground, or a moving train. Frames in which the first law holds are called inertial frames. Okay? Any frame moving with constant velocity relative to an inertial frame is also inertial. Right? But an accelerating or a rotating frame is not inertial. So whenever we use the first law, we work from an inertial frame. Clear? And the good news: a frame fixed to the ground is very nearly inertial, for most problems. So the ground is our usual frame. With me?

4:20Quick check: which frames are inertial?

Quick check. Four frames on screen, labelled a, b, c and d in brackets. Frame a: a lift moving up at constant speed. Frame b: a car going round a curve at constant speed. Frame c: a train that is braking. And frame d: a spacecraft drifting with its engines off, far from all stars. Which of these are inertial? Okay, let's check. Frame c, the braking train: its speed changes, so it accelerates. Now frame b, the car on the curve. Constant speed, so many students call it inertial. No, no, wait! Its direction keeps changing, so its velocity changes. It is accelerating too. Remember, constant velocity means constant speed and constant direction. So the inertial frames are a and d: the lift at constant speed, and the drifting spacecraft. Perfect!

5:15Example 1: the third force for constant velocity

First example. Two forces act on a particle: two i cap plus three j cap newtons, and minus five i cap plus j cap newtons. The i cap and j cap, letters with little caps, are unit vectors along the x and y axes, and capital N is the newton, the unit of force. There is also a third force, and the particle moves with constant velocity. Find the third force. Pause the video, and try it first. Done? Okay, let's check. Call the forces F one, F two and F three; the small numbers below are just labels. Constant velocity, so by the first law the net force is zero: F one plus F two plus F three equals the zero vector. See, we used the law backwards, from velocity to force. Okay? Now add the first two, part by part. The i cap parts: two minus five, minus three. The j cap parts: three plus one, four. So F one plus F two is minus three i cap plus four j cap. Now tell me, what must F three be? Yes, exactly! F three must cancel this sum, so it is the negative of F one plus F two. Just flip both signs: three i cap minus four j cap, newtons. That's it! And its magnitude, written with the two straight bars, is the square root of three squared plus four squared. Five newtons. Very good!

6:51Example 2: acceleration when a 6 N force is removed

Now a slightly harder one. So, a body of mass two kilograms, the k g on screen, is at rest under several forces. One of them is six newtons, due east. That force is suddenly removed. Find the acceleration of the body. Pause and try. Hint: what was the net force before the removal? Done? Okay, let's check. We are not told the other forces, but we don't need them! Use the first law. Before the removal, the body is at rest, so the net force is zero. That means the other forces together balance the six newtons east. Okay? So the other forces add up to six newtons, due west: same size, opposite direction. Now the east force is removed. Which way will the body accelerate? West! Many students say east, where the force was. But that force is gone; what remains is six newtons due west. Right? Finally, acceleration a equals net force F over mass m; we do this properly in the next lesson. Six over two: three metres per second squared, due west. The m s to the minus two on screen means metres per second squared. Perfect!

8:10Quick revision: inertia, the first law, zero net force

So, quick revision. Inertia: a body's tendency to keep its state of rest or uniform motion, and mass measures it. First law, in an inertial frame: the net force is zero if and only if the velocity is constant. And zero net force means zero acceleration, not zero velocity. Now go and try the practice problems on this page. All the best!