Changing Motion

Circular Motion

When an object moves at a constant speed in a circular path, the velocity is constantly changing.

As seen in the diagram below, the length of the arrows for velocity are the same (same magnitude) but the direction is different! Recall that velocity is a vector quantity, so since the direction continuously changes the velocity changes too.Changing Motion, figure 1

Inertia

From the equation F = ma, it is clear to see that if we increase the mass, we have to increase the force applied in order to maintain a constant acceleration. This was mentioned in the previous learning episode.

Inertia is a measure of how difficult it is to change the velocity of an object, including a zero value.

In order to change the velocity you need to change the acceleration and in order for that to occur, a change in force.

The mass in the equation F = ma is sometimes referred to as inertial mass for this reason.

Newton’s Third Law

The final law of Newton’s laws is as follows:

If object A exerts a force on another object B, then object B exerts a force on object A that is exactly the same size and in the opposite direction.

  • The forces have to act on different bodies
  • The forces have to be the same type (usually gravitational, contact or tension)
  • The forces have to be the same size
  • The forces have to be in the opposite directionChanging Motion, figure 1

Momentum

Momentum is a measure of the mass __and velocity __of an object. A massive object and a tiny object can both have the same momentum, but the larger object must be travelling very slowly and the smaller object travelling really quickly. You need to recall and apply this equation:Changing Motion, figure 1

Collisions involve two objects (two cars, two balls, a ball and a bat etc) colliding with each other. For this type of question calculate the momentum before and after separately and then make sure they are the same.Changing Motion, figure 2Changing Motion, figure 3

Impulse

We can use Newton’s second law to define impulse; the time it takes for a force to be exerted over an object.Changing Motion, figure 1

  • F = Force (N)
  • t = Time (s)
  • m = Mass (kg)
  • u = Initial velocity (m/s)
  • v = Final velocity (m/s)
Calculate the momentum of an athlete of mass 60 kg running at a velocity of 10 m/s?
600kgm/s
Explanation: p = m x v p = 60 x 10 = 600kgm/s
Calculate the force required to stop a 750kg car moving at 20m/s in 30s
500N
Calculate the mass of a stationary car that is hit by a 600kg car that was moving at 10m/s. The cars move together after the collision at 2m/s.
2400kg