12PHYS - Mechanics

Finn LeSueur

2021

Aaron is painting the outside of his house. He is standing on a \(3.5m\) long plank with a support at each end. The plank weighs \(4.8kg\). He is standing \(0.8m\) from the left side and he weighs \(63kg\).

- Draw a diagram to illustrate the situation
- Calculate the support force provided by Support A (left) and Support B (right).

The motion of an object moving in a circular path.

e.g. Satellites in orbit, car driving around a corner, discus thrower, cricket bowler.

- How do we calculate circumference?
**Whakatika**: \(C = 2\pi r\)- Where \(r\) is the radius of the circle

- Frequency is
**the number of rotations in one second**. - It is given the symbol \(f\) and measured in \(s^{-1}\) (per second).

- Period is
**the time taken to do one revolution**. - It is given the symbol \(T\) and is measured in \(s\) (seconds).
- Period and frequency are inversely related via this equation
- \(T = \frac{1}{f}\)

- Velocity is always given by \(v = \frac{d}{t}\)
- On a circle, \(d = C = 2 \pi r\)
- On a circle, \(t = T = \frac{1}{f}\)
- Therefore, circular velocity is \(v = \frac{2\pi r}{T}\)

**If the radius is 2m, find the**: circumference,- and speed

**If the radius is 2m, find the**: circumference,- \(C = 2 \pi r = 2 \pi 2 = 12.57m\)

- period,
- \(T = 12s\)

- frequency
- \(f = \frac{1}{T} = \frac{1}{12} = 0.083^{-s}\)

- and speed
- \(v = \frac{d}{t} = \frac{12.57}{12} = 1.0475ms^{-1}\)

- Is speed constant?
- Is velocity constant?

**Is speed constant?**- Speed is constant, because the
**magnitude**of the velocity is constant.

- Speed is constant, because the
**Is velocity constant?**- Velocity is not constant, because even though the magnitude is constant, the direction is changing.

\[\begin{aligned} & a_{c} = \frac{v^{2}}{r} \newline \end{aligned}\]An object undergoing circular motion is always accelerating towards the center of the circle. Therefore, because the direction is changing, the velocity is changing. Therefore the object is always accelerating, even if its speed is constant.

- An ice skater performs a 720 degree jump. The outside of their shoulders rotate with a frequency of \(1.5s^{-1}\).
**Calculate the period of their rotations**. - If their shoulders are \(30cm\) from their center of rotation, calculate their linear velocity.
- Draw a diagram illustrating the things you know about their circle of rotation.

**An ice skater performs a 720 degree jump. The outside of their shoulders rotate with a frequency of \(1.5s^{-1}\). Calculate the period of their rotations.**

\(T = \frac{1}{f} = \frac{1}{1.5} = 0.667s\)**If their shoulders are \(30cm\) from their center of rotation, calculate their linear velocity.**

\(v=\frac{2 \pi r}{T} = \frac{2 \pi 0.3}{0.667} = 2.826ms^{-1}\)**Draw a diagram illustrating the things you know about their circle of rotation.**

- Newton’s Laws of Motion tell us that
**an acceleration is always caused by an unbalanced force (non-zero net force).** - Therefore, centripetal (
*center-seeking*) acceleration is caused by an unbalanced force which continuously pulls the object towards the center.**Centripetal (**.*center-seeking*) force - Net force and acceleration vectors point in the same direction.

- Centripetal force acts inwards towards the center of the circle, while the velocity acts along a tangent to the circle at all times.
- Therefore, if the centripetal force is removed, the object will move in a straight line tangent to the circle

- Mathieu is swinging a bucket of water above his head. It weighs, \(8kg\) and has a horizontal speed of \(4ms^{-1}\) in a circle of radius \(1m\).
**Calculate the force required to keep the bucket moving in a circle.****Knowns, Unknowns, Formula, Substitute, Solve**

NB: From 2:30 to 5:25.

- During a hammer throw, a steel ball is swung horizontally with a speed of \(10ms^{-1}\) in a circle of radius \(2m\). \(350N\) of tension force is required.
**Calculate the mass of the steel ball.****Knowns, Unknowns, Formula, Substitute, Solve**