6. Motion in a circle Flashcards
Formula for Angular Displacement and its units?
θ = s / r
te-ta = arc length / radius
Units: rad
Formula for Angular Velocity and its units?
ω = θ / t
angular velocity = te-ta / time taken
v = rω
velocity = radius x angular velocity
Who provides centripetal force for the planets orbiting our solar system and what happens when there is no centripetal force?
The gravity of the sun exerts an attraction force on the planets around it providing the centripetal force, when the attraction force is not sufficient (or in the case of a string, breaks), there will be no centripetal force for the planets and they will fly off in a direction tangent to the circular path.
Is a resultant force present in a uniform circular motion?
Yes. Linear speed in a uniform circular motion remains unchanged however, velocity changes as direction is always changing, by Newton’s second law, there is a resultant force acting on it, hence the motion is accelerated.
The 2 Formulas for centripetal acceleration.
a = v^2 / r
acceleration = linear velocity^2 / radius
a = ω^2 x r
acceleration = angular velocity^2 x radius
(Can be derived with ω = v / r)
The 2 Formulas for Centripetal Force?
.
.
Hint: recall F = ma
F = mv^2 / r
Centripetal force = (mass x velocity ^2) / radius
F = mrω^2
Centripetal force = mass x radius x angular velocity^2
On roads with high speed limit, the roads are banked, explain how banking allow the speed limit to be increased.
Without road banking, the centripetal force on the car is provided solely by friction exerted by the roads on the tires. When the road is banked, the centripetal force on the car is provided by the horizontal components of friction, and the normal contact force exerted by the road on the tires. The maximum centripetal force that the car can now experience is greater than the maximum friction. Hence the speed limit can increase as mass and radius remains constant.
