Circular Motion

Centripetal Acceleration

**Centripetal Acceleration** – if something
has centripetal acceleration it means that it's moving with constant speed
around a circle and is always accelerating toward the center; also the
acceleration is always at a right angle to the velocity. Centripetal acceleration
is when the acceleration is "inward seeking".

Centripetal Acceleration Formula

**Example 1**

A runner moving at a speed of 8.8 m/s rounds a bend with a radius of 25 m. What is the centripetal acceleration?

**Example 2**

An airplane traveling at 201 m/s makes a turn. What is the smallest radius of the circular path that the pilot can make and keep the centripetal acceleration under 5.0 m/s^2?

**Example 3**

A beetle standing on the edge of a 12 in vinyl record of "Stop Making Sense" by the Talking Heads is whirling around at 33.33 rotations per minute. Compute the magnitude of the creature's centripetal acceleration.

Centripetal Force

**Example 4**

A car racing on a flat track travels at 22 m/s around a curve with a 56 m radius. Find the car’s centripetal acceleration. What minimum coefficient of static friction between the tires and road is necessary for the car to round the curve without slipping?

**Example 5**

A 45 kg merry-go-round worker stands on the ride’s platform 6.3 m from the center. If her speed as she goes around the circle is 4.1 m/s, what is the force of friction necessary to keep her from falling off the platform?

**Example 6**

A hammer thrower at a track-and-field meet whirls around at a rate of 2.0 revolutions per second, revolving a 16 lb ball at the end of a cable that gives it a 6.0 ft effective radius. Compute the inward force that must be exerted on the ball.

Newton's Law of Universal Gravitation

**Gravitational Force** – the mutual force of
attraction between two particles of matter.

Newton's Law of Universal Gravitation

**Example 7**

Two bowling balls each have a mass of 6.8 kg. They are located next to each other with their centers 21.8 cm apart. What gravitational force to they exert on each other?

**Example 8**

The gravitational force between two electrons that are 1.00 m apart is 5.54 x 10^-71 N. Find the mass of an electron.

**Example 9**

Consider two subatomic particles, an electron and a proton, which have masses of 9.1 x 10^–31 kg and 1.7 x 10^–27 kg, respectively. When separated by a distance of 5.3 x 10^–11 m, as they are in a hydrogen atom, the electrical attraction (Fe) between them is 8.2 x 10^–8 N. Compare this with the correcponding gravitational interaction. How many times larger is Fe than Fg?