Chp 6: circular motion Flashcards
Define period
time taken for one complete revolution
Define angular velocity
the rate of change of angular displacement with respect to time.
Define frequency
the number of complete revolutions made per unit time.
Properties of centripetal force
- Centripetal force is a resultant force, not a new force
- Centripetal force is always directed perpendicular to the direction of motion
& towards the centre of the circular path.
Use Newton’s laws of motion to explain why a body moving with uniform speed in a circle must experience a force towards the centre of the circle
- Despite the speed being constant, the direction of the object changes, hence velocity changes.
- So, there must be acceleration. By N2L, there is a net force acting on the object.
- Since speed is constant, the net force cannot have a component in the direction of motion, hence the net force must act towards the centre of the circle.
Define angular displacement
the angle an object makes with respect to a reference line.
Define radian
the angle subtended by an arc length equal to the radius of the arc.
During uniform circular motion, why the speed of the object does not change?
This is because the centripetal force is always directly perpendicular to the direction of motion. Thus, displacement in the direction of centripetal force is zero. Therefore there is no work done by the centripetal force. The kinetic energy of the object does not change.
State in terms of the forces acting on an object, one condition necessary for the object to move in a circular path at constant speed.
The resultant force acting on the object must be always perpendicular to the direction of motion and acts towards the centre of the circular path.
Why does an object moving in a uniform circular motion has constant speed but is accelerating?
As the object moves in a circular motion its direction changes. Since velocity is a vector which includes both magnitude and direction, its velocity changes despite speed being constant. Since acceleration is the rate of change of velocity, the object must be accelerating.
Use Newton’s laws of motion to explain why an object moving with uniform speed in a circle must experience a force towards the centre of the circle.
The direction of the object changes continuously and hence there is a change in velocity of the object. Based on Newton’s 1st law, this means that there must be a net force acting on the object. Since the speed remains unchanged, no work is done by this force, this force cannot have a component tangential to the circle. This implies that the force is perpendicular to the velocity/displacement of object (so points towards the centre of circle).
Using a rope, a bucket of water is swung in a vertical circle. At the top of the circle, the speed of the bucket is v and the bucket is upside down at this instant. Explain qualitatively why the water in the bucket does not fall out.
If the speed of rotation is high enough, the weight of the water alone in the bucket is not enough to provide for the centripetal force required, including when bucket is at highest point. The shortfall in centripetal force is supplied by the reaction force due to the bottom of the bucket on the water to keep it moving in the vertical circle. (W + N provides for Fc). By Newton’s third law, the water pushes against the bottom of the bucket and thus stays in the bucket
A stone is attached to a string. The stone rotates in a circle, with its centre at C, at constant speed in a vertical plane, as shown in the figure below. Suggest why, in practice, it would be difficult to maintain a constant angular speed of the stone.
Speed of stone tends to change as it rises or drops in a vertical circle due to changes in GPE and KE. Hence to maintain a constant angular velocity, w, energy needs to be gradually supplied and withdrawn accordingly. Since this is a string and not a rigid rod, it is not possible for energy to be gradually supplied and withdrawn accordingly in order to maintain constant angular velocity.
A rider makes a left turn on a rough surface banked at 20° to the horizontal as shown below. Assume that the frictional forces remain the same.
(a) Explain how the banked surface assists the rider in travelling around the corner at a higher speed
(b) Given that the cyclist now travels at a faster speed, state and explain whether it will move up or down the road.
a) For a surface which is banked, the component of the normal reaction parallel to the road is now an additional source of the centripetal force (along with the component of the friction parallel to the road), thus provides for part of the required centripetal force and hence the rider relies less on friction to provide the greater centripetal force required to turn the corner at a higher speed without slipping.
b) The cyclist will move up the track. When speed increases, the required centripetal force will be larger. Since weight, angle and hence normal reaction forces are constant, 𝑁𝑐𝑜𝑠𝜃 = 𝑚𝑔 & 𝑁𝑠𝑖𝑛𝜃 = 𝑚𝑣 2 𝑟 , the cyclist will move up the track to increase the radius of circular motion so that the demand for centripetal force stays constant
A communications satellite moves at constant angular speed in a circular orbit around the Earth. What is the work done by the gravitational force in one revolution? Explain your answer.
The gravitational force does no work. The gravitational force provides for the centripetal force for the satellite’s circular motion. Since the satellite moves constant angular speed, it undergoes a uniform circular motion hence the centripetal force (and hence the gravitational force) is always perpendicular to the displacement and velocity of the satellite and hence, there is no force acting in the direction of motion
