5.2 Flashcards
Define the radian
The angle subtended when the arc length is equal to the radius
Define the period of an object in circular motion
The time taken for one complete revolution
Define the frequency of an object in circular motion
The number of compete revolutions per second
State an equation for angular velocity in terms of:
a) frequency
b) period
ω = 2πf
ω = 2π/T
State an equation to show how you convert from:
a) radians to degrees
b) degrees to radians
a) angles in degrees = 180/π x angle in radians
b) angle in radians = π/180 x angle in degrees
Explain what causes a body to move in a circular path
An object is caused to move in a circular path if a constant net force is applied perpendicular to the direction of its velocity.
Derive:
v = ωr
v = distance/ time
For an object moving in a circle, the distance moved is equal to the circumference of a circle.
v = 2πr/t
We already know that:
ω =2π/t
Therefore:
v = ωr
Define centripetal force; include an equation in your answer.
A force that keeps a body moving with constant speed in a circular path
F = mv^2/r
Describe an experiment that could be used to investigate circular motion and verify the equation.
F = mv^2/r
Tie a 1 m length of string to a rubber bung.
Attach the other end of the string to a 100g mass and thread through a glass tube.
Rotate the rubber bung in a horizontal circle, ensuring that its radius remains constant. Measure the radius of the orbit using a metre rule.
Measure the mass of the rubber bung using a balance.
Measure the time taken to complete 10 rotations of the rubber bung using a stopwatch.
Calculate the period of one orbit by dividing the time taken for 10 orbits by 10.
Calculate the velocity of the orbit using:
v =2πr/T
where R is the radius of the orbit and T is the time period.
Calculate the centripetal force using:
F =mv^2/r
The centripetal force should be equal to the weight of the 100 g mass (0.98 N).
Repeat this experiment with different masses.
Plot a graph of v2against r. The graph will show a direct proportion relationship.
Name the type of accleration caused by an object moving in a circle and state its direction
Centripetal acceleration
Direction = towards the centre of the circle
State an equation for centripetal acceleration in terms of:
a) linear velocity
b) angular velocity
a = v^2/r
a = ω^2r
Explain why, when being driven around a tight bend in the curve, a racing car will need to increase its velocity.
An increase in velocity causes the centripetal force to increase. The centripetal force is provided by the friction of the tyres on the road. This increase in friction between the tyres and the road ensures the car stays in contact with the road. Hence as velocity increases, friction increases and the car stays on the road.
