3B2 Uniform Circular Motion Flashcards
Describe uniform circular motion through the concepts of net force and centripetal acceleration.
Define:
Uniform circular motion
Movement in a circular path at a constant speed.
Although the speed is constant, the direction of motion changes, causing acceleration.
List characteristics of uniform circular motion.
- Constant speed
- Changing velocity
- Acceleration directed towards the center
- Net force directed towards the center
Despite constant speed, the direction change results in varying velocity.
Name one real-world example of uniform circular motion.
A satellite orbiting Earth.
Gravity acts as the centripetal force for satellites in orbit.
True or False:
In uniform circular motion, velocity is constant.
False
Velocity changes direction continuously, even if the speed remains constant.
What are the two velocities calculated in uniform circular motion?
- Tangential velocity
- Rotational (angular) velocity
In uniform circular motion, the rotational velocity is constant, while the tangential velocity remains constant in magnitude but continuously changes direction.
Define:
Tangential speed
The linear speed of an object moving along a circular path.
Tangential speed depends on the object’s distance from the center of rotation and angular velocity. This is represented by the formula v = ωr, where ω equals radians per second and r is the radius.
Define:
Rotational velocity
Number of rotations or revolutions an object completes per unit of time.
It is measured in units such as radians per second (rad/s) or revolutions per minute (rpm).
True or False:
Tangential speed is independent of angular velocity.
False
Tangential speed is directly proportional to angular velocity (v =r⋅ω).
Fill in the blank:
Tangential speed ______ with the distance from the center of rotation.
increases
Tangential speed is given by v=r⋅ω, where r is radius and ω is angular velocity
Fill in the blank:
Tangential speed is ______ to the radius of the circular path.
perpendicular
Tangential speed determines how fast the object moves along the circle.
Name a real-world example where tangential speed varies with distance from the center of rotation.
- A spinning record player
- Merry-go-rounds
- Car wheels
The edge of the record moves faster tangentially than points closer to the center.
Compare the tangential speed at the base and the tip of a cone rolling on a flat surface.
The base has a higher tangential speed than the tip.
Tangential speed increases with radius from the center of rotation.
How does the conical shape of train wheels affect tangential speed?
The larger radius on one side creates a higher tangential speed, which helps the train navigate curves.
This design keeps the train aligned on the tracks during turns.
What is the period in uniform circular motion?
The time taken for one complete revolution.
Period is related to tangential speed by T=2𝜋𝑟/v.
What is the relationship between angular velocity (ω) and period (T) in circular motion?
ω= 2π/T
Angular velocity is the rate of change of angular displacement and is inversely proportional to the period.
What are the two components of linear acceleration in circular motion?
- Tangential acceleration (changes speed)
- Centripetal acceleration (changes direction)
In uniform circular motion, tangential acceleration is zero, while centripetal acceleration is always present.
What causes tangential acceleration in rotational motion?
A change in the object’s angular velocity, which results in a change in the object’s tangential velocity.
Tangential acceleration is given by a =r⋅α, where α is angular acceleration.
Define:
Centripetal acceleration
The inward acceleration experienced by an object moving in a circular path.
It is directed towards the center of the circle.
Fill in the blank:
The centripetal acceleration measures the rate of change in _______ direction for an object in circular motion.
velocity’s
While the magnitude of velocity remains constant in uniform circular motion, its direction continuously changes due to centripetal acceleration.
What causes centripetal acceleration?
The continuous change in direction of velocity toward the center of the circle.
Centripetal acceleration is given by ac=v²/r
Fill in the blank:
As the radius of the circular path increases, centripetal acceleration ______.
decreases
Radius and acceleration are inversely proportional.
Fill in the blank:
Centripetal force always acts ______ to the circle of motion.
inward
This inward force is necessary to keep the object in circular motion.
What is the formula for centripetal acceleration?
ac = v² / r
Acceleration increases with higher speed or smaller radius.
What is the unit of measurement for centripetal acceleration?
m/s²
Acceleration measures the rate of change of velocity.
Name an example of centripetal acceleration in everyday life.
- Merry-go-round
- Roller coaster loops
- Ball on a string
- Lab centrifuge
The acceleration keeps them moving in a circular path.
What is centrifugal force?
The apparent outward force felt by an object moving in a circle due to inertia.
It is not a real force; rather, it is the effect of inertia acting on the object.
What is the formula for centripetal force?
Fc = mv² / r
Where ‘Fc’ is centripetal force, ‘m’ is mass, ‘v’ is velocity, and ‘r’ is the radius.
How are centripetal force and centripetal acceleration related in circular motion?
Centripetal force causes centripetal acceleration, and their magnitude is proportional, as described by F=ma.
This relationship shows that the net force acting toward the center is essential for maintaining circular motion.
How does the radius of the circular path affect centripetal force?
A larger radius requires less centripetal force for the same speed.
Centripetal force is inversely proportional to radius.
What happens if the centripetal force is removed?
The object will move in a straight-line path from the point of release.
This is due to the object’s inertia.
What force acts as the centripetal force for planets orbiting the Sun?
Gravity
Gravity provides the necessary centripetal force to maintain elliptical orbits.
Name a situation where friction provides centripetal force.
A car turning on a curved road.
Friction between tires and the road provides the inward force.
What happens to the centripetal force if the speed of an object in circular motion doubles?
The centripetal force increases by a factor of 4.
Centripetal force is proportional to v², so doubling the speed quadruples the force.
Explain how a bicycle wheel’s rotational motion aids its movement.
The tangential speed of the wheels propels the bicycle forward, converting rotational motion into linear motion.
Gear ratios affect the rotational speed and tangential speed of the wheels.
Why do larger gears on a bicycle increase the tangential speed of the wheels?
Larger gears increase the effective radius, increasing the tangential force applied to the wheels.
This principle explains how gear ratios affect speed and force.
Why do runners on a circular track feel different speeds depending on their lane?
Tangential speed is higher in outer lanes due to the larger radius of rotation.
This is why longer distances are run in the outer lanes of a track.
True or False:
Friction, tension or gravity can provide the centripetal force necessary for circular motion
True
Centripetal force is not a separate force but the net inward force resulting from other forces like tension, friction, or gravity.
Fill in the Blank:
The net force that keeps an object moving in a circular path is called the _______ force.
centripetal
This force is responsible for continuously changing the direction of the object’s velocity.
A car moves around a circular track with a radius of 50 m at a constant speed of 10 m/s. What is the centripetal acceleration of the car?
ac = v² / r= (10m/s)² / (50m)= 2m/s²
Centripetal acceleration depends on the square of velocity and the radius of the circular path.
How does physics keep roller coaster cars from detaching from the track?
The centripetal force prevents the cars from moving tangentially off the loop by pulling them toward the center of the circular path.
This force is often provided by the track’s normal force and gravity.
A 0.5 kg ball is swung in a circle with a radius of 2 m at a speed of 4 m/s. What is the centripetal force acting on the ball?
Fc = mv² / r=[(0.5 kg)(4 m/s)²]/(2 m)=4N
The centripetal force depends on mass, velocity, and radius of the circle.
True or False:
The larger the radius of a circular path, the smaller the required centripetal force for the same speed.
True
Centripetal force is inversely proportional to the radius .
What role does gravity play as a centripetal force in planetary orbits?
Gravity acts as the centripetal force that keeps planets in their elliptical orbits around the sun.
This relationship is described by Kepler’s laws of planetary motion.
Fill in the Blank:
If the radius of a circular path decreases while maintaining the same speed, the centripetal force _______.
increases
Fc ∝ 1/r, so a smaller radius requires more force to maintain circular motion.
True or False:
The centripetal force acting on an object decreases as the period of rotation increases.
True
A longer period corresponds to a lower angular velocity, which reduces centripetal force (Fc =4π²r/T²)
Why does the net force required for circular motion increase with a shorter period?
A shorter period increases angular velocity, which raises centripetal acceleration, thus increasing net force.
Centripetal force is proportional to the square of angular velocity.
How does the frequency of an object in circular motion affect its centripetal acceleration?
Higher frequency increases centripetal acceleration because ac=(2πf)² r
Frequency is directly proportional to centripetal acceleration for a given radius.
Fill in the Blank:
Centripetal acceleration is inversely proportional to the square of the _______ of an object in uniform circular motion.
period (T)
The relationship can be expressed as ac=4π²r/T², showing how a shorter period increases the centripetal acceleration.
