3B2 Uniform Circular Motion

Question 1

Define:

Uniform circular motion

Answer 1

Movement in a circular path at a constant speed.

Although the speed is constant, the direction of motion changes, causing acceleration.

Question 2

List characteristics of uniform circular motion.

Answer 2

• 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.

Question 3

Name one real-world example of uniform circular motion.

Answer 3

A satellite orbiting Earth.

Gravity acts as the centripetal force for satellites in orbit.

Question 4

True or False:

In uniform circular motion, velocity is constant.

Answer 4

False

Velocity changes direction continuously, even if the speed remains constant.

Question 5

What are the two velocities calculated in uniform circular motion?

Answer 5

• 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.

Question 6

Define:

Tangential speed

Answer 6

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.

Question 7

Define:

Rotational velocity

Answer 7

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).

Question 8

True or False:

Tangential speed is independent of angular velocity.

Answer 8

False

Tangential speed is directly proportional to angular velocity (v =r⋅ω).

Question 9

Fill in the blank:

Tangential speed ______ with the distance from the center of rotation.

Answer 9

increases

Tangential speed is given by v=r⋅ω, where r is radius and ω is angular velocity

Question 10

Fill in the blank:

Tangential speed is ______ to the radius of the circular path.

Answer 10

perpendicular

Tangential speed determines how fast the object moves along the circle.

Question 11

Name a real-world example where tangential speed varies with distance from the center of rotation.

Answer 11

• A spinning record player
• Merry-go-rounds
• Car wheels

The edge of the record moves faster tangentially than points closer to the center.

Question 12

Compare the tangential speed at the base and the tip of a cone rolling on a flat surface.

Answer 12

The base has a higher tangential speed than the tip.

Tangential speed increases with radius from the center of rotation.

Question 13

How does the conical shape of train wheels affect tangential speed?

Answer 13

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.

Question 14

What is the period in uniform circular motion?

Answer 14

The time taken for one complete revolution.

Period is related to tangential speed by T=2𝜋𝑟/v.

Question 15

What is the relationship between angular velocity (ω) and period (T) in circular motion?

Answer 15

ω= 2π/T

Angular velocity is the rate of change of angular displacement and is inversely proportional to the period.

Question 16

What are the two components of linear acceleration in circular motion?

Answer 16

• Tangential acceleration (changes speed)
• Centripetal acceleration (changes direction)

In uniform circular motion, tangential acceleration is zero, while centripetal acceleration is always present.

Question 17

What causes tangential acceleration in rotational motion?

Answer 17

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.

Question 18

Define:

Centripetal acceleration

Answer 18

The inward acceleration experienced by an object moving in a circular path.

It is directed towards the center of the circle.

Question 19

Fill in the blank:

The centripetal acceleration measures the rate of change in _______ direction for an object in circular motion.

Answer 19

velocity’s

While the magnitude of velocity remains constant in uniform circular motion, its direction continuously changes due to centripetal acceleration.

Question 20

What causes centripetal acceleration?

Answer 20

The continuous change in direction of velocity toward the center of the circle.

Centripetal acceleration is given by ac=v²/r

Question 21

Fill in the blank:

As the radius of the circular path increases, centripetal acceleration ______.

Answer 21

decreases

Radius and acceleration are inversely proportional.

Question 22

Fill in the blank:

Centripetal force always acts ______ to the circle of motion.

Answer 22

inward

This inward force is necessary to keep the object in circular motion.

Question 23

What is the formula for centripetal acceleration?

Answer 23

ac = v² / r

Acceleration increases with higher speed or smaller radius.

Question 24

What is the unit of measurement for centripetal acceleration?

Answer 24

m/s²

Acceleration measures the rate of change of velocity.

Question 25

Name an **example of centripetal acceleration** in everyday life.

Answer 25

* Merry-go-round * Roller coaster loops * Ball on a string * Lab centrifuge ## Footnote The acceleration keeps them moving in a circular path.

Question 26

What is **centrifugal force**?

Answer 26

The **apparent outward force** felt by an object moving in a circle due to inertia. ## Footnote It is not a real force; rather, it is the effect of inertia acting on the object.

Question 27

What is the **formula** for **centripetal force**?

Answer 27

Fc = mv² / r ## Footnote Where 'Fc' is centripetal force, 'm' is mass, 'v' is velocity, and 'r' is the radius.

Question 28

How are **centripetal force** and **centripetal acceleration** related in circular motion?

Answer 28

**Centripetal force causes centripetal acceleration**, and their magnitude is proportional, as described by F=ma. ## Footnote This relationship shows that the net force acting toward the center is essential for maintaining circular motion.

Question 29

How does the **radius** of the circular path affect **centripetal force**?

Answer 29

A **larger radius requires less centripetal force** for the same speed. ## Footnote Centripetal force is inversely proportional to radius.

Question 30

What happens if the **centripetal force is removed**?

Answer 30

The object will move in a **straight-line path** from the point of release. ## Footnote This is due to the object's inertia.

Question 31

What force acts as the **centripetal force** for **planets orbiting the Sun**?

Answer 31

Gravity ## Footnote Gravity provides the necessary centripetal force to maintain elliptical orbits.

Question 32

Name a situation where **friction** provides **centripetal force**.

Answer 32

A **car turning** on a curved road. ## Footnote Friction between tires and the road provides the inward force.

Question 33

What happens to the centripetal force if the **speed** of an object in circular motion **doubles**?

Answer 33

The centripetal force **increases by a factor of 4**. ## Footnote Centripetal force is proportional to v², so doubling the speed quadruples the force.

Question 34

Explain how a **bicycle wheel's rotational motion** aids its movement.

Answer 34

The **tangential speed** of the wheels propels the bicycle forward, converting rotational motion into linear motion. ## Footnote Gear ratios affect the rotational speed and tangential speed of the wheels.

Question 35

Why do larger gears on a bicycle increase the **tangential speed** of the wheels?

Answer 35

Larger gears **increase the effective radius**, increasing the tangential force applied to the wheels. ## Footnote This principle explains how gear ratios affect speed and force.

Question 36

Why do runners on a **circular track** feel different speeds depending on their lane?

Answer 36

Tangential speed is **higher in outer lanes** due to the larger radius of rotation. ## Footnote This is why longer distances are run in the outer lanes of a track.

Question 37

# True or False: Friction, tension or gravity can provide the **centripetal force** necessary for circular motion

Answer 37

True ## Footnote **Centripetal force is not a separate force** but the net inward force resulting from other forces like tension, friction, or gravity.

Question 38

# Fill in the Blank: The **net force** that keeps an object moving in a circular path is called the \_\_\_\_\_\_\_ force.

Answer 38

centripetal ## Footnote This force is responsible for continuously changing the direction of the object’s velocity.

Question 39

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?

Answer 39

ac = v² / r= (10m/s)² / (50m)= 2m/s² ## Footnote Centripetal acceleration depends on the square of velocity and the radius of the circular path.

Question 40

How does physics keep **roller coaster cars** from detaching from the track?

Answer 40

The centripetal force prevents the cars from moving tangentially off the loop by **pulling them toward the center of the circular path**. ## Footnote This force is often provided by the track's normal force and gravity.

Question 41

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?

Answer 41

Fc = mv² / r=[(0.5 kg)(4 m/s)²]/(2 m)=4N ## Footnote The centripetal force depends on mass, velocity, and radius of the circle.

Question 42

# True or False: The larger the radius of a circular path, the smaller the required centripetal force for the **same speed**.

Answer 42

True ## Footnote Centripetal force is inversely proportional to the radius .

Question 43

What role does **gravity** play as a **centripetal force** in planetary orbits?

Answer 43

Gravity acts as the centripetal force that **keeps planets in their elliptical orbits** around the sun. ## Footnote This relationship is described by Kepler's laws of planetary motion.

Question 44

# Fill in the Blank: If the radius of a circular path decreases while maintaining the **same speed**, the centripetal force \_\_\_\_\_\_\_.

Answer 44

increases ## Footnote Fc ∝ 1/r, so a smaller radius requires more force to maintain circular motion.

Question 45

# True or False: The **centripetal force** acting on an object decreases as the **period** of rotation increases.

Answer 45

True ## Footnote A longer period corresponds to a lower angular velocity, which reduces centripetal force (Fc =4π²r/T²)

Question 46

Why does the **net force** required for circular motion increase with a shorter **period**?

Answer 46

A shorter period **increases angular velocity**, which raises centripetal acceleration, thus increasing net force. ## Footnote Centripetal force is proportional to the square of angular velocity.

Question 47

How does the **frequency** of an object in circular motion affect its **centripetal acceleration**?

Answer 47

Higher frequency **increases centripetal acceleration** because ac=(2πf)² r ## Footnote Frequency is directly proportional to centripetal acceleration for a given radius.

Question 48

# Fill in the Blank: **Centripetal acceleration** is **inversely proportional** to the square of the \_\_\_\_\_\_\_ of an object in uniform circular motion.

Answer 48

period (T) ## Footnote The relationship can be expressed as ac=4π²r/T², showing how a shorter period increases the centripetal acceleration.