Circular motion

A whirling ball constantly accelerates.

The string connected to the ball pulls it towards the centre.

In the case of a whirling [blank_start]ball[blank_end], a [blank_start]larger[blank_end] force is needed if (i) the [blank_start]speed[blank_end] v of the ball is [blank_start]increased[blank_end] (ii) the [blank_start]radius[blank_end] r of the circle is [blank_start]decreased[blank_end] (iii) the [blank_start]mass[blank_end] m of the ball is [blank_start]increased[blank_end]

In the case of a whirling ball, [blank_start]F = mv^2/r[blank_end], when m is [blank_start]mass[blank_end], v is [blank_start]speed[blank_end], and r is the [blank_start]radius[blank_end].

The [blank_start]force[blank_end] which acts towards the [blank_start]centre[blank_end] and keeps a body moving in a [blank_start]circular[blank_end] path is called the [blank_start]centripetal force[blank_end].

In the case of a whirling ball, if the force is [blank_start]greater[blank_end] than the string can bear, the string [blank_start]breaks[blank_end] and the ball [blank_start]flies[blank_end] off with [blank_start]steady[blank_end] speed in a [blank_start]straight[blank_end] line along the [blank_start]tangent[blank_end].

When dealing with [blank_start]centripetal[blank_end] force, [blank_start]friction[blank_end] can act as an [blank_start]accelerating[blank_end] force.

In the case of a [blank_start]banked[blank_end] road, the [blank_start]horizontal[blank_end] effect of the [blank_start]contact[blank_end] force N is the [blank_start]centripetal[blank_end] force.

In the case of a [blank_start]satellite[blank_end] orbiting the [blank_start]earth[blank_end], the [blank_start]centripetal[blank_end] force is provided by [blank_start]gravity[blank_end].

For a circular orbit, the orbital period [blank_start]T = 2πr/v[blank_end].

Satellites in high orbits have longer periods than those in low orbits.

The moon has an orbital period of 28 days.

Geostationary satellites don't have an orbit high above the equator.

The orbital period for geostationary satellites is 24 hours.

Geostationary satellites travel with the same speed as the Earth rotates.

Monitoring satellites circle the Earth rapidly in low polar orbits.

The orbital period for monitoring satellites is 90 minutes.

Monitoring satellites are widely used in weather forecasting.