Define time period.
The time elapsed during one full oscillation.
Define frequency.
The number of rotations per unit time.
Define velocity.
The rate of change of displacement.
Define angular velocity.
The rate of change of angle.
Give an equation for angular velocity based upon time period and theta.
omega = theta/T
How do linear and angular velocity vary with radius?
Linear velocity decreases as a greater distance (circumference) is covered per unit time.
Angular velocity remains constant.
Give equations relation angular velocity and frequency/time period.
omega = 2pif
omega = 2*pi/T
Give an equation relation linear and angular velocity.
v=omega*r
How can we make an object describe a circular path of motion?
Apply a force directly perpendicular to the direction of it’s velocity.
What is a centripetal force?
A force acting towards the centre of a particle’s circular path, perpendicular to the direction of it’s motion.
Why is no work done when an object moves in a circular path?
The force applied is perpendicular to the direction of motion - no distance traveled in direction of force
Why is velocity constant in circular motion?
No work is done thus Ek is constant.
Why do objects in circular motion accelerate, despite their velocity not changing?
The object’s direction is constantly changing. Velocity is a vector quantity thus it is changing, so the object accelerates.
What happens when the force providing the centripetal acceleration of an object is less than the centripetal force required to describe a circular path?
The object does not move in a. circular path; it begins to spiral outward.
Give the equation for centripetal acceleration.
a=omega^2*r
Give an equation for centripetal force.
F=mv^2/r = momega2*r
When a car orbits a roundabout, what provides the centripetal force required to do so?
Friction due to contact between the tyres and the road.
How can we use centripetal forces to explain understeer in a car?
- As speed increases, centripetal force required to maintain circular path rises
- Friction has a maximum value given by mu*R
- This will eventually become less than reqd centripetal force
- The car’s path spirals and you understeer (very dangerous situation to be in!!!)
Why is a greater centripetal force generated on a banked road?
The horizontal component of friction is added to by the horizontal component of the normal reaction force
For a conical pendulum setup, what provides the centripetal force?
Horizontal component of tension = Tsin theta
For a conical pendulum to remain level, what criteria must be satisfied?
Tcos theta = mg so resultant vertical component of force is equal to zero
What happens when we increase the speed of a conical pendulum?
- More centripetal force required
- Tsin theta increases
- Thus theta increases so cos theta decreases
- T must increase to maintain Tcos theta = mg for decreasing cos theta
Why is a conical pendulum never completely horizontal?
If theta = 90 then T cos theta = 0, which can never equal mg given a pendulum bob must have mass!!
Describe the resultant force at the top of a Ferris wheel in vertical circular motion.
mv^2/r = mg-R
