Uniform Circular Motion

Condition for circular motion

� A body needs a Centripetal force to make a curved motion or move in a circle

If you identify the nature of this Force, the calculations become easy.

Centripetal acceleration

�  ac = v2/r

⇒  Centripetal Force Fc = mac= mv2/r

V V

V V

F

Examples

Examples

� String tied to a string What is the centripetal Force?

Centripetal Force provided by the Tension Force

What happens to tension in this case?

Examples

� Moon going around earth What is the centripetal Force?

Centripetal Force provided by the Gravitational Forces between earth and the moon

Examples

� Ball rolling through a hole What is the centripetal Force?

Centripetal Force provided by the Normal Force

Examples � Car going along a curve What is the centripetal Force?

Equations for a Car on curve

�  The centripetal force is provided by the Frictional force specifically by Static Friction Fs

- When a car turns to the left why do you slide to the right?

If you were an astronaut on a spaceship going around earth, would you slide outwards and cling on to the wall of the spaceship? Why/ Why not?

Problem - UCM

Curved portions of highways are always banked (tilted) to prevent cars from sliding off the highway. When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding. When the highway is wet, however, the frictional force may be negligible, and banking is then essential. Figure represents a car of mass m as it moves at a constant speed v of 20 m/s around a banked circular track of radius R = 190 m. (It is a normal car, rather than a race car, which means any vertical force from the passing air is negligible.) If the frictional force from the track is negligible, what bank angle θ prevents sliding? (Ans - 12deg)

Problems - Drag A raindrop with radius R = 1.5 mm falls from a cloud that is

at height h = 1200 m above the ground. The drag

coefficient C for the drop is 0.60. Assume that the drop is

spherical throughout its fall. The density of water ρw is

1000 kg/m3, and the density of air ρa is 1.2 kg/m3.

1) The raindrop reaches terminal speed after falling just a

few meters. What is the terminal speed? (27 Km/hr) 2) What would be the drop's speed just before impact if there were no drag force? ( 550 km/hr)