Uniform circular motion

The horses on a merry-go-round always rotate at the same speed, describing circles.

1. a) What type of motion do they describe?
2. b) Explain in your own words what the period and frequency of this motion are.

A wheel completes $50$ turns in $10\ \text{s}$.

1. a) Calculate its period, in seconds.
2. b) Calculate its frequency, in hertz ($\text{Hz}$).

A blender motor rotates at a frequency of $2\ \text{Hz}$.

1. a) What is its period?
2. b) How many turns does it complete in one minute?

Observe the second hand of an analogue clock.

1. a) What is its period, that is, how long does it take to make one complete turn?
2. b) How many turns does it make in one hour?

A bicycle travels at $6\ \text{m/s}$ and its wheels have a radius of $0,3\ \text{m}$.

1. a) Calculate the rotational period of the wheels, that is, the time they take to complete one turn. Hint: in one turn, a point on the wheel travels $2 \pi r$.
2. b) Calculate the rotational frequency, in $\text{Hz}$.

Take $\pi = 3,14$ and round the results to one decimal place.

The drum of a washing machine spins at $1200\ \text{rpm}$ and has a radius of $0,25\ \text{m}$.

1. a) Express its frequency in hertz.
2. b) Calculate its period.
3. c) Calculate the linear speed of a point on the edge of the drum. Take $\pi = 3,14$.

The second hand of a wall clock is $0,15\ \text{m}$ long.

1. a) Calculate the linear speed of its tip, in $\text{m/s}$. Take $\pi = 3,14$ and round to three decimal places.
2. b) Express the result in $\text{cm/s}$, to one decimal place.
3. c) An ant walks at $2\ \text{cm/s}$. Which is faster, the ant or the tip of the second hand? Justify your answer using calculations.

Two friends get on a merry-go-round with a period of $8\ \text{s}$: one at $2\ \text{m}$ from the centre and the other at $5\ \text{m}$.

1. a) Calculate the linear speed of each person. Take $\pi = 3,14$ and round to one decimal place.
2. b) Calculate the ratio of the two speeds and compare it with the ratio of the radii.
3. c) Calculate the angular velocity of the merry-go-round using $\omega = \frac{2 \pi}{T}$ and explain why it is the same for both friends even though their linear speeds are different.

A cyclist rides at $6,28\ \text{m/s}$ on a bicycle whose wheels have a radius of $0,5\ \text{m}$.

1. a) Calculate the rotation frequency of the wheels. Take $\pi = 3,14$.
2. b) How many revolutions does each wheel make in $5\ \text{min}$ of pedalling?
3. c) What distance does the cyclist cover in that time? Check that it equals the number of revolutions multiplied by the circumference of the wheel.