Circular Motion Flashcards
What is Uniform circular motion
Motion along a circular path in which there is no change in speed, only in direction.
In Uniform circular motion what is the direction of constant velocity and constant force?
Constant velocity is tangent to the path
Constant force is towards the center
What happens when the central force is removed in uniform circular motion?
The ball will continue moving in a straight line. Centripetal force is needed to change direction
Is there an outward force acting on a ball in uniform circular motion?
No, because the ball is moving at a tangent to the path. When the force is removed, it will continue in a straight line not outwards
What are the key conceprts of acceleration in uniform circular motion?
- Speed is constant, but direction is always changing.
- Velocity is a vector and can be impacted by magnitude or direction or both.
-If the direction is changing, therefore velocity is changing so there is acceleration.
-If acceleration is present, there must be a force acting on the object (Newtonβs 1/2 law)
-The direction of the force is always towards the center there for the direction of acceleration is also towards the center
What is centripetal force?
A force acting on an object moving in a circular path which is directed toward the centre around which the object moves.
What is the equation for linear and angular speed during uniform circular motion?
Linear speed, v = d/t = s/t (ms-1)
Angular speed, w = angle/time = 0/t (rad/s)
If the object has completed a full cycle (distance = circumference) in time T s, then the time T is known as Time Period.
Linear speed, v = distance/time = 2ππ/T
Angular speed, w = angle/ time = 2π/π
π ππππππππ 2π/π ππ ππππππ π ππππ πππππ’ππ, π£=πΟ
A particle moves round the circumference of a circle with radius 10π at a speed of 20ππ ^(β1).
Calculate its angular speed.
v = rw
w = v/r = 20/10
=2
How do you resolve x and y components?
ysinπ
xcosβ‘π
What is the accelearation of an object moving on a circular path with constant angular speed?
rπ^2 directed towards the centre of the circle.
The position vector of P at time π‘ π =rcosπ and rsinπ
At constant speed: ππ/ππ‘=π
Let π‘=0 when P is at A β π=ππ‘
βπ=πcosβ‘ππ‘ and ππ ππππ‘
differentiating s gives v =(βππ sinβ‘ππ‘ and ππ πππ ππ‘)
differentiating v gives a=
π=(βππ^2 cosβ‘ππ‘ and βππ^2 π ππ ππ‘) = βπ^2 (π cosβ‘ππ‘ and π π ππ ππ‘)=βπ^2 π
What is another way of calculating acceleration in circular motion?
π=ππ^2 = π£^2/π
We know that π£=ππβ π=π£/π
Also π=ππ^2
Substituting for π gives: π=π(π£/π)^2=π£^2/π
A particle is moving on a horizontal circular path of radius 30cm with a constant angular speed of 4πππ π ^(β1). Calculate the acceleration of the particle.
π=ππ^2=0.3Γ4^2=4.8ππ ^(β2)
What is the equation for acceleration towards the centre (centripetal acceleration)?
ac= v^2/R
Fc = mac
= mv^2/R
A 3-kg rock swings in a circle of radius 5 m. If its constant speed is 8 m/s, what is the centripetal acceleration?
ac = 12.8 m/s
Fc = 38.4 N
A skater moves with 15 m/s in a circle of radius 30 m. The ice exerts a central force of 450 N. What is the mass of the skater?
m = 60
What is the nature of centripetal force Fc?
The centripetal force Fc is that of static friction fs
How do you calculate the maximum speed for negotiating a turn without slipping
Fc = Fs
Fc = mv^2/R
fs = ΞΌs x mg
v = βΞΌsgR
Where v is maximum speed without slipping
How can optimum banking angle be calculated?
By resolving the vectors using trig
Nsin0 = mv^2/R
Ncos0 = mg
Tan 0 = v^2/gR
What is does Newtonβs second law state in relation to circular motion?
N2L states that all accelerating objects require a net or resultant force.
F = ma
What direction are centripetal force and acceleration acting in?
Towards the center of the circle
Is there work being done during uniform circular motion?
No, Since the net force is perpendicular to the direction of motion and work done = Force x distance, no work is being done on the force. This is also why there is no change in speed.
What factors will cause an increase in the resultant centripetal force?
- The object rotates faster ( Has a larger angular velocity.)
- If the object has more mass
- If the object is further from the center of the circle
