A radian (rad) is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

Define angular displacement .

Angular displacement is the change in angle, in radians, of a body as it rotates around a circle.

How many radians are there in a complete circle (360°)?

A complete circle is equal to 2π radians .

To convert an angle from degrees into radians, multiply the angle in degrees by ..........

To convert an angle from degrees into radians, multiply the angle in degrees by π ⁄ 180 .

True or False? One radian is a larger angle than one degree.

True. Since 2π radians = 360°, one radian is equivalent to about 57.3°, which is much larger than one degree.

Frequency , f , is the number of complete oscillations per unit time, measured in hertz (Hz).

Define time period , T .

Time period , T , is the time taken for one complete oscillation, in seconds.

One complete oscillation is the time taken for the oscillator to pass the equilibrium from one side and back again fully from the ..........

One complete oscillation is the time taken for the oscillator to pass the equilibrium from one side and back again fully from the other side .

Define angular speed , ω.

Angular speed is the rate of change of angular displacement with respect to time.

What is the difference between angular speed and angular velocity?

Angular speed is a scalar quantity, while angular velocity is the same quantity expressed as a vector , since it also has a direction.

What are the units of angular speed?

Angular speed is measured in rad s -1 .

For a fixed linear speed, an object rotating further from the centre of a circle (a larger radius) has a .......... angular velocity.

For a fixed linear speed, an object rotating further from the centre of a circle (a larger radius) has a smaller angular velocity.

True or False? An object moving with uniform circular motion has a constant velocity, because its speed does not change.

False. Although the speed is constant, the direction is constantly changing, so the velocity is not constant and the object is accelerating.

Define centripetal force .

Centripetal force is the resultant force towards the centre of the circle required to keep a body in uniform circular motion; it is always directed towards the centre of the body's rotation.

In what direction does the centripetal force act, relative to an object's velocity?

At 90° (perpendicular) to the velocity, directed towards the centre of the circle.

Why must there be a net force on an object moving in a circle at constant speed?

Because the direction of its velocity is constantly changing, so it is accelerating; by Newton's second law , acceleration requires a resultant force.

Is centripetal force a distinct type of force in its own right?

No. Centripetal force is not a separate force — it is whatever resultant force (for example tension, gravity, friction, or normal contact force) provides the net force towards the centre.

The net (centripetal) force on an object in circular motion always acts towards the .......... of the circle.

The net (centripetal) force on an object in circular motion always acts towards the centre of the circle.

True or False? A “centrifugal force” pushes objects outwards, away from the centre, during uniform circular motion.

False. There is no real outward force acting on the object; the only force present is the centripetal force , acting towards the centre of the circle.

Define linear velocity (in circular motion).

Linear velocity is the velocity of an object rotating in uniform circular motion, with respect to linear displacement, as opposed to angular displacement.

For a constant angular speed, how does increasing the radius of the circular path affect the linear speed?

The linear speed increases ; v is directly proportional to r .

Does angular speed depend on the radius of the circular path?

No. Angular speed (and angular velocity) does not depend on the radius; only the linear speed depends on the radius.

For an object to move with uniform circular motion, a net force must act at .......... to its constant linear speed.

For an object to move with uniform circular motion, a net force must act at right angles (90°) to its constant linear speed.

True or False? In uniform circular motion, an object has zero acceleration because its speed is constant.

False. The object still accelerates because its direction is constantly changing, even though its speed stays constant.

Define centripetal acceleration .

Centripetal acceleration is the acceleration of an object towards the centre of a circle when it moves (rotates) around the circle at a constant speed.

In what direction does centripetal acceleration act, relative to an object's velocity?

Towards the centre of the circle, perpendicular to the object's velocity.

What provides the centripetal force in the circular motion investigation?

The weight, Mg , of the hanging mass M creates constant tension in the string, which provides the centripetal force .

In the circular motion experiment, the radius, r , is the length of string between the bung and the .......... .

In the circular motion experiment, the radius, r , is the length of string between the bung and the glass tube .

How do the time period and centripetal force change as the radius, r , is increased?

The time period, T, increases, but the centripetal force, F, remains the same.

True or False? In a vertical circle, the tension in the string stays constant throughout the motion.

False. The tension varies continuously , reaching a maximum at the bottom and a minimum at the top of the circle.

Why does the string go slack if the bung moves too slowly at the top of a vertical circle?

The required tension would become negative , which is impossible, so the string goes slack .

A LevelPhysicsOCRFlashcards5. Newtonian World & AstrophysicsCircular Motion

Circular Motion (OCR A Level Physics): Flashcards

Exam code: H556

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Cards in this collection (47)

Define radian.
A radian (rad) is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.
Define angular displacement.
Angular displacement is the change in angle, in radians, of a body as it rotates around a circle.
What equation gives angular displacement, θ, in terms of arc length, S, and radius, r?
$θ = \frac{S}{r}$
How many radians are there in a complete circle (360°)?
A complete circle is equal to 2π radians.
To convert an angle from degrees into radians, multiply the angle in degrees by ..........
To convert an angle from degrees into radians, multiply the angle in degrees by π ⁄ 180.
True or False?
One radian is a larger angle than one degree.
True.
Since 2π radians = 360°, one radian is equivalent to about 57.3°, which is much larger than one degree.
Define frequency.
Frequency, f, is the number of complete oscillations per unit time, measured in hertz (Hz).
Define time period, T.
Time period, T, is the time taken for one complete oscillation, in seconds.
What equation relates frequency, f, and time period, T?
$f = \frac{1}{T}$
What is the speed of an object moving in a circle of radius r, in terms of the time period, T?
$v = \frac{2 π r}{T}$
One complete oscillation is the time taken for the oscillator to pass the equilibrium from one side and back again fully from the ..........
One complete oscillation is the time taken for the oscillator to pass the equilibrium from one side and back again fully from the other side.
True or False?
Frequency and time period are directly proportional to each other.
False.
Frequency and time period are inversely proportional: $f = \frac{1}{T}$ , so as T increases, f decreases.
Define angular speed, ω.
Angular speed is the rate of change of angular displacement with respect to time.
What equation gives angular speed in terms of the change in angular displacement and time?
$ω = \frac{Δ θ}{Δ t}$
What is the difference between angular speed and angular velocity?
Angular speed is a scalar quantity, while angular velocity is the same quantity expressed as a vector, since it also has a direction.
What are the units of angular speed?
Angular speed is measured in rad s^-1.
How can angular speed be written in terms of the time period, T, or frequency, f?
$ω = \frac{2 π}{T} = 2 π f$
For a fixed linear speed, an object rotating further from the centre of a circle (a larger radius) has a .......... angular velocity.
For a fixed linear speed, an object rotating further from the centre of a circle (a larger radius) has a smaller angular velocity.
True or False?
An object moving with uniform circular motion has a constant velocity, because its speed does not change.
False.
Although the speed is constant, the direction is constantly changing, so the velocity is not constant and the object is accelerating.
Define centripetal force.
Centripetal force is the resultant force towards the centre of the circle required to keep a body in uniform circular motion; it is always directed towards the centre of the body's rotation.
In what direction does the centripetal force act, relative to an object's velocity?
At 90° (perpendicular) to the velocity, directed towards the centre of the circle.
Why must there be a net force on an object moving in a circle at constant speed?
Because the direction of its velocity is constantly changing, so it is accelerating; by Newton's second law, acceleration requires a resultant force.
What two equations can be used to calculate centripetal force, F?
$F = \frac{m v^{2}}{r}$ and $F = m r ω^{2}$
Is centripetal force a distinct type of force in its own right?
No. Centripetal force is not a separate force — it is whatever resultant force (for example tension, gravity, friction, or normal contact force) provides the net force towards the centre.
The net (centripetal) force on an object in circular motion always acts towards the .......... of the circle.
The net (centripetal) force on an object in circular motion always acts towards the centre of the circle.
True or False?
A “centrifugal force” pushes objects outwards, away from the centre, during uniform circular motion.
False.
There is no real outward force acting on the object; the only force present is the centripetal force, acting towards the centre of the circle.
Define linear velocity (in circular motion).
Linear velocity is the velocity of an object rotating in uniform circular motion, with respect to linear displacement, as opposed to angular displacement.
What equation relates linear speed, v, angular speed, ω, and radius, r?
$v = r ω$
For a constant angular speed, how does increasing the radius of the circular path affect the linear speed?
The linear speed increases; v is directly proportional to r.
Does angular speed depend on the radius of the circular path?
No. Angular speed (and angular velocity) does not depend on the radius; only the linear speed depends on the radius.
For an object to move with uniform circular motion, a net force must act at .......... to its constant linear speed.
For an object to move with uniform circular motion, a net force must act at right angles (90°) to its constant linear speed.
True or False?
In uniform circular motion, an object has zero acceleration because its speed is constant.
False.
The object still accelerates because its direction is constantly changing, even though its speed stays constant.
Define centripetal acceleration.
Centripetal acceleration is the acceleration of an object towards the centre of a circle when it moves (rotates) around the circle at a constant speed.
What equation gives centripetal acceleration in terms of linear speed, v, and radius, r?
$a = \frac{v^{2}}{r}$
What equation gives centripetal acceleration in terms of radius, r, and angular speed, ω?
$a = r ω^{2}$
What equation gives centripetal acceleration in terms of linear speed, v, and angular speed, ω?
$a = v ω$
In what direction does centripetal acceleration act, relative to an object's velocity?
Towards the centre of the circle, perpendicular to the object's velocity.
If both the radius and the angular speed of a rotating object are doubled, the centripetal acceleration ( $a = r ω^{2}$ ) increases by a factor of ..........
If both the radius and the angular speed of a rotating object are doubled, the centripetal acceleration increases by a factor of eight.
True or False?
Centripetal acceleration and centripetal force act in the same direction.
True.
Both are directed towards the centre of the circle, perpendicular to the velocity, consistent with Newton's second law ( $F = m a$ ).
What provides the centripetal force in the circular motion investigation?
The weight, Mg, of the hanging mass M creates constant tension in the string, which provides the centripetal force.
How is the angular velocity, ω, of the bung determined experimentally?
$ω = \frac{2 π}{T}$
where T is the measured time period of one rotation.
In the circular motion experiment, the radius, r, is the length of string between the bung and the ...........
In the circular motion experiment, the radius, r, is the length of string between the bung and the glass tube.
What relationship should be found between the centripetal force and the hanging mass?
$F_{c} \approx M g$
The calculated centripetal force should approximately equal the weight of the hanging mass.
How do the time period and centripetal force change as the radius, r, is increased?
The time period, T, increases, but the centripetal force, F, remains the same.
True or False?
In a vertical circle, the tension in the string stays constant throughout the motion.
False.
The tension varies continuously, reaching a maximum at the bottom and a minimum at the top of the circle.
Why does the string go slack if the bung moves too slowly at the top of a vertical circle?
The required tension would become negative, which is impossible, so the string goes slack.
State the tension equations at the bottom and top of a vertical circle.
$F_{T m a x} = \frac{m v^{2}}{r} + m g$ at the bottom (tension overcomes weight)
$F_{T m i n} = \frac{m v^{2}}{r} - m g$ at the top (tension and weight act together)

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