6.1 Circular Motion

Question 1

Marks: 1

A particle rotates clockwise in a horizontal circle of radius r with a constant angular velocity ω. The particle is at S at time zero and at P at time t. Q represents the projection of point P onto the diameter through S. Measured with respect to the centre of orbit O, the displacement, linear velocity and linear acceleration of Q along OS are x, v and a respectively.

6-1-sl-mcq-hard-q1-phy

Which of the following sets of expressions is correct?

	$x$	v	a
A.	$r \cos ω t$	$- r ω \sin ω t$	$r ω^{2} \cos ω t$
B.	$r \cos ω t$	$- r ω \sin ω t$	$- r ω^{2} \cos ω t$
C.	$r \sin ω t$	$- r ω \cos ω t$	$- r ω^{2} \sin ω t$
D.	$r \sin ω t$	$r ω \cos ω t$	$r ω^{2} \sin ω t$

Key Concepts

Centripetal Force

Question 2

Marks: 1

A simple pendulum consists of a bob of mass m at the end of a light inextensible thread of length d. The bob swings through point Y with velocity v and comes to an instantaneous rest at point X, where the string is just taut.

6-1-sl-mcq-hard-q2-phy

What is the tension in the thread as the bob passes point Y?

Key Concepts

Centripetal Force

Question 3

Marks: 1

A particle travels in a circular path in a magnetic field with radius x and centripetal acceleration a.

What is the time taken for 15 complete rotations?

$2 π \sqrt{\frac{x}{a}}$
$30 π \sqrt{\frac{x}{a}}$
$2 π \sqrt{\frac{a}{x}}$
$30 π \sqrt{\frac{a}{x}}$

Key Concepts

Properties of Circular Motion
Centripetal Acceleration

Question 4

Marks: 1

A mass m₁ is attached to one end of a light extensible string of length x. When the mass rotates with a linear speed v in a horizontal plane, an extension Δx is obtained.

Which of the following shows the correct expression for another mass m₂, if it is attached to the same light extensible string and rotated with the same linear speed v but rotates at twice the radius as that produced by m₁?

$m_{2} = \frac{2 m_{1} (x + ∆ x)}{∆ x}$
$m_{2} = \frac{2 m_{1} (2 x + ∆ x)}{∆ x}$
$m_{2} = \frac{4 m_{1} (x + ∆ x)}{∆ x}$
$m_{2} = \frac{2 m_{1} (x + 2 ∆ x)}{∆ x}$

Key Concepts

Centripetal Acceleration

Question 5

Marks: 1

Two bobs A and B, of equal mass, are connected by a light inextensible string of length l.

6-1-sl-mcq-hard-q5-phy

Bob A is tied to a nail at the centre of a smooth table by another light, inextensible string of length 3l. The bobs are then set into uniform motion on the surface of the table with the same angular velocity.

What is the ratio of the tension in the string connecting bob A and B to that in the string connecting bob A to the nail?

Key Concepts

Centripetal Force

Question 6

Marks: 1

An aircraft moves in a horizontal plane at a constant linear speed v and makes a turn of radius r.

6-1-sl-mcq-hard-q6-phy

Which of the following expressions is true for the tilt angle θ?

You may wish to use the relationship:

$\tan θ = \frac{\sin θ}{\cos θ}$

$θ \propto r$
$θ \propto \frac{1}{r}$
$\tan θ \propto r$
$\tan θ \propto \frac{1}{r}$

Key Concepts

Centripetal Force

Question 7

Marks: 1

The maximum speed for a car to safely move round a corner when the road is dry is 10 m s^–1. The maximum frictional force between the road surface and the wheels of the car is halved when the road is wet.

What is the maximum safe speed for a car to go round the corner when the road is wet?

$\sqrt{2}$ m s^–1
$2 \sqrt{2}$ m s^–1
$5 \sqrt{2}$ m s^–1
$10 \sqrt{2}$ m s^–1

Key Concepts

Centripetal Force

Question 8

Marks: 1

A conker attached to a string is whirled in a vertical circle at constant speed.

Which of the following correctly shows the variation of the tension T in the string with the angular displacement θ?

6-1-sl-mcq-hard-q8-phy

Key Concepts

Centripetal Force
Applications of Circular Motion

Question 9

Marks: 1

A small object is attached to a string and whirled in a vertical circle at a constant speed. The magnitude of the net force F on the object at the top of the circle is given by:

$F_{t o p} = T + m g$

Where T is the tension in the string, m is the object's mass and g is the acceleration of free fall.

The magnitude of the net force on the object at the bottom of the circle is given by:

$F_{b o t t o m} = T - m g$

Which of the following statements is correct?

The net force on the object at the bottom of the loop is greater than the net force at the top
The net force on the object decreases as the object moves from the bottom to the top of the loop
The net force on the object at the top of the loop is greater than the net force at the bottom
The net force on the object is the same at the top and at the bottom of the loop

Key Concepts

Applications of Circular Motion
Centripetal Force

Question 10

Marks: 1

Two masses m₁ and m₂ are fixed on a horizontal circular rotating platform. m₂ is half as massive as m₁ and is fixed at a distance three times as far from the centre as m₁. The net force on m₁ is F₁ and the net force on m₂ is F₂.

Which of the following statements is correct?

$F_{1} = \frac{1}{2} F_{2}$
$F_{1} = \frac{1}{3} F_{2}$
$F_{1} = \frac{2}{3} F_{2}$
$F_{1} = 2 F_{2}$

Key Concepts

Centripetal Force

DP IB Physics: HL

Topic Questions

6.1 Circular Motion

Question 1

Key Concepts

Question 2

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Question 3

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Question 4

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Question 5

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Question 6

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Question 7

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Question 8

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Question 9

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Question 10

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