IB Questionbank

User interface language: English | Español

Date	November 2019	Marks available	2	Reference code	19N.3.SL.TZ0.5
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Show that	Question number	5	Adapted from	N/A

Question

A flywheel is made of a solid disk with a mass M of 5.00 kg mounted on a small radial axle. The mass of the axle is negligible. The radius R of the disk is 6.00 cm and the radius r of the axle is 1.20 cm.

A string of negligible thickness is wound around the axle. The string is pulled by an electric motor that exerts a vertical tension force T on the flywheel. The diagram shows the forces acting on the flywheel. W is the weight and N is the normal reaction force from the support of the flywheel.

The moment of inertia of the flywheel about the axis is $I = \frac{1}{2} M R^{2}$ .

The flywheel is initially at rest. At time t = 0 the motor is switched on and a time-varying tension force acts on the flywheel. The torque $Γ$ exerted on the flywheel by the tension force in the string varies with t as shown on the graph.

At t = 5.00 s the string becomes fully unwound and it disconnects from the flywheel. The flywheel remains spinning around the axle.

State the torque provided by the force W about the axis of the flywheel.

[1]

Identify the physical quantity represented by the area under the graph.

[1]

b(i).

Show that the angular velocity of the flywheel at t = 5.00 s is 200 rad s^–1.

[2]

b(ii).

Calculate the maximum tension in the string.

[1]

b(iii).

The flywheel is in translational equilibrium. Distinguish between translational equilibrium and rotational equilibrium.

[2]

c(i).

At t = 5.00 s the flywheel is spinning with angular velocity 200 rad s^–1. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 10³ revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.

[3]

c(ii).

Markscheme

zero ✔

«change in» angular momentum ✔

NOTE: Allow angular impulse.

b(i).

use of L = lω = area under graph = 1.80 «kg m²s^–1» ✔

rearranges «to give ω= area/I» 1.80 = 0.5 × 5.00 × 0.060²× ω ✔

«to get ω = 200 rad s^–1»

b(ii).

$« \frac{0.40}{0.012} = » 33.3 N$ ✔

b(iii).

translational equilibrium is when the sum of all the forces on a body is zero ✔

rotational equilibrium is when the sum of all the torques on a body is zero ✔

c(i).

ALTERNATIVE 1

$0 = 200^{2} + 2 \times α \times 2 π \times 8000$ ✔

$α = « - » 0.398 « rad s^{- 2} »$ ✔

torque = $α I = 0.398 \times (0.5 \times 5.00 \times 0 . 060^{2}) = 3.58 \times 10^{- 3} « N m »$ ✔

ALTERNATIVE 2

change in kinetic energy $= « - » 0.5 \times (0.5 \times 5.00 \times 0 . 060^{2}) \times 200^{2} = « - » 180 « J »$ ✔

identifies work done = change in KE ✔

torque = $\frac{W}{θ} = \frac{180}{2 π \times 8000} = 3.58 \times 10^{- 3} « N m »$ ✔

c(ii).

Examiners report

[N/A]

b(i).

[N/A]

b(ii).

[N/A]

b(iii).

[N/A]

c(i).

[N/A]

c(ii).

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Core topics) » B.1 – Rigid bodies and rotational dynamics

Show 52 related questions

17M.3.SL.TZ2.6c.i:
Determine the final angular speed of the probe–satellite system.
18M.3.SL.TZ1.6d.i:
Explain why the angular speed will increase.
16N.3.SL.TZ0.9: The diagram shows two methods of pedalling a bicycle using a force F. In method 1 the...
18M.3.SL.TZ2.6a.iii:
Determine the angular velocity of the wheel at B.
18M.3.SL.TZ2.6b.ii:
Describe the effect of F on the angular speed of the wheel.
18N.3.SL.TZ0.6b.ii:
After time t the rod makes an angle θ with the horizontal. Outline why the equation $\theta = \frac{1}{2}\alpha {t^2}$ cannot be used to find the time it takes θ to become $\frac{\pi }{2}$ (that is for the rod to become vertical for the first time).
18N.3.SL.TZ0.6c.ii: At the instant the rod becomes vertical calculate the angular momentum of the rod.
18N.3.SL.TZ0.6a: Calculate the force the support exerts on the rod.
18M.3.SL.TZ2.6a.ii:
In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s^–1 after its displacement.
17N.3.SL.TZ0.7c: Calculate the acceleration of the hoop when θ = 20°. Assume that the hoop continues to roll...
18M.3.SL.TZ1.6b.ii:
Calculate, for the merry-go-round after one revolution, the angular momentum.
17M.3.SL.TZ2.6a.i:
Deduce the linear acceleration of the centre of mass of the probe.
16N.3.SL.TZ0.8a:
The velocity of the falling object is 1.89 m s^–1 at 3.98 s. Calculate the average angular acceleration of the flywheel.
18N.3.SL.TZ0.6c.i:
At the instant the rod becomes vertical show that the angular speed is ω = 2.43 rad s^–1.
18N.3.SL.TZ0.6b.i:
Calculate, in rad s^–2, the initial angular acceleration $\alpha$ of the rod.
17N.3.SL.TZ0.6a: Explain what is meant by proper length.
17N.3.SL.TZ0.7a: On the diagram, draw and label the forces acting on the hoop.
19N.3.SL.TZ0.5a: State the torque provided by the force W about the axis of the flywheel.
19N.3.SL.TZ0.5b(iii):
Calculate the maximum tension in the string.
19N.3.SL.TZ0.5c(i): The flywheel is in translational equilibrium. Distinguish between translational equilibrium...
19N.3.SL.TZ0.5b(i): Identify the physical quantity represented by the area under the graph.
17N.3.SL.TZ0.7d:
State the relationship between the force of friction and the angle of the incline.
16N.3.SL.TZ0.8b:
Show that the torque acting on the flywheel is about 0.3 Nm.
17M.3.SL.TZ1.5b.ii:
Calculate the number of revolutions made by the system before it comes to rest.
18M.3.SL.TZ2.6a.i:
The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.
18M.3.SL.TZ1.6c:
Calculate the new angular speed of the rotating system.
19M.3.SL.TZ2.8b:
Calculate F.
18M.3.SL.TZ1.6b.i:
Calculate, for the merry-go-round after one revolution, the angular speed.
20N.3.SL.TZ0.6a:
Show that the final angular velocity of the bar is about $3 rad s^{- 1}$ .
16N.3.SL.TZ0.8c:
(i) Calculate the tension in the string.

(ii) Determine the mass m of the falling object.
17N.3.SL.TZ0.7e:
The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.
19N.3.SL.TZ0.5c(ii):
At t = 5.00 s the flywheel is spinning with angular velocity 200 rad s^–1. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 10³ revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.
19M.3.SL.TZ2.9a:
Show that the total kinetic energy E_k of the sphere when it rolls, without slipping, at speed v is ${E_{\text{K}}} = \frac{7}{{10}}m{v^2}$ .
20N.3.SL.TZ0.6d:
The torque is removed. The bar comes to rest in $30$ complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.
20N.3.SL.TZ0.6b:
Draw the variation with time $t$ of the angular displacement $θ$ of the bar during the acceleration.
20N.3.SL.TZ0.7b: Explain the changes to the rotational kinetic energy in the person-turntable system.
20N.3.SL.TZ0.7a:
Explain the direction in which the person-turntable system starts to rotate.
20N.3.SL.TZ0.6c:
Calculate the torque acting on the bar while it is accelerating.
20N.3.SL.TZ0.8:
A solid sphere of radius $r$ and mass $m$ is released from rest and rolls down a slope, without slipping. The vertical height of the slope is $h$ . The moment of inertia $I$ of this sphere about an axis through its centre is $\frac{2}{5} m r^{2}$ .

Show that the linear velocity $v$ of the sphere as it leaves the slope is $\sqrt{\frac{10 g h}{7}}$ .
17M.3.SL.TZ2.6b:
The forces act for 2.00 s. Show that the final angular speed of the probe is about 16 rad $\,$ s^–1.
17N.3.SL.TZ0.7b:
Show that the linear acceleration a of the hoop is given by the equation shown.

a = $\frac{{g \times \sin q}}{2}$
18M.3.SL.TZ1.6d.ii:
Calculate the work done by the child in moving from the edge to the centre.
19M.3.SL.TZ2.8a: Outline why the normal force acting on the ladder at the point of contact with the wall is...
17M.3.SL.TZ1.5a.i:
Write down an expression, in terms of M, v and R, for the angular momentum of the system about the vertical axis just before the collision.
17M.3.SL.TZ1.5a.ii:
Just after the collision the system begins to rotate about the vertical axis with angular velocity ω. Show that the angular momentum of the system is equal to $\frac{4}{3}M{R^2}\omega$ .
17M.3.SL.TZ1.5a.iii:
Hence, show that $\omega = \frac{v}{{4R}}$ .
17M.3.SL.TZ1.5b.i:
Show that the angular deceleration of the system is 0.043 rad $\,$ s^–2.
17M.3.SL.TZ2.6a.ii:
Calculate the resultant torque about the axis of the probe.
17M.3.SL.TZ1.5a.iv:
Determine in terms of M and v the energy lost during the collision.
17M.3.SL.TZ2.6c.ii:
Calculate the loss of rotational kinetic energy due to the linking of the probe with the satellite.
18M.3.SL.TZ1.6a:
Show that the angular acceleration of the merry-go-round is 0.2 rad s^–2.
19M.3.SL.TZ2.9b:
A solid sphere of mass 1.5 kg is rolling, without slipping, on a horizontal surface with a speed of 0.50 m s^-1. The sphere then rolls, without slipping, down a ramp to reach a horizontal surface that is 45 cm lower.

Calculate the speed of the sphere at the bottom of the ramp.

Hide related questions

Option B: Engineering physics » Option B: Engineering physics (Core topics)

Option B: Engineering physics

Question

Markscheme

Examiners report

Syllabus sections

View options