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A bar rotates horizontally about its centre, reaching a maximum angular velocity in six
complete rotations from rest. The bar has a constant angular acceleration of 0.110rads*.
The moment of inertia of the bar about the axis of rotation is 0.0216 kgm’.
——
(a) Show that the final angular velocity of the bar is about 3rads"*. 2]
(b) Draw the variation with time t of the angular displacement 0 of the bar during the
acceleration. tt]
@lrad
tis
(c) Calculate the torque acting on the bar while it is accelerating. (1) =13- 8820-6503
(Option B, question 8 continued)
(4) 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. [2]
(Option B continues on the following page) 9.
The first diagram shows a person standing on a turntable which can rotate freely. The person
is stationary and holding a bicycle wheel. The wheel rotates anticlockwise when seen from above.
turntable can
rotate freely
The wheel is flipped, as shown in the second diagram, so that it rotates clockwise when seen
from above.
(a) Explain the direction in which the person-tumtable system starts to rotate. 13) -15- 8820-6503
(Option B, question 9 continued)
(b) Explain the changes to the rotational kinetic energy in the person-tumtable system. 2]
40. A.solid sphere of radius rand 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 / of this sphere about an
axis through its centre is 2 mr’
Show that the linear velocity v of the sphere as it leaves the slope is ‘eh : 3]
(Option B continues on the following page) -14- N19/4/PHY SI/HP3/ENG/TZO/XX
Option B — Engineering physics
7. Aflywheel is made of a solid disk with a mass M of 5.00kg mounted on a small radial axle.
The mass of the axle is negligible. The radius R of the disk is 6.00cm and the radius r of the
axle is 1.20cm.
Asstring 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. Wis the weight and N is the normal reaction force from the support of
the flywheel.
not to scale
A
to the motor |
'
string,
axle.
qo ap
r
disk w
The moment of inertia of the flywheel about the axis is J = fur.
(a) State the torque provided by the force W about the axis of the flywheel. [1] -15- N19/4/PHYSI/HP3/ENG/TZO/XX
(Option B, question 7 continued)
(b) 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 exerted on the flywheel by the tension
force in the string varies with t as shown on the graph.
50)
40
T/102Nm 30
20
10
0 1.00 2.00 3.00 4.00 5.00
(i) Identify the physical quantity represented by the area under the graph. ti
(ii) Show that the angular velocity of the flywheel at f = 5.00s is 200rads“*. ea)
(iii) Calculate the maximum tension in the string. i -16- N19/4/PHYSWHP3/ENG/TZO/XX
(Option B, question 7 continued)
(c)_ Att=5.00s the string becomes fully unwound and it disconnects from the flywheel.
The flywheel remains spinning around the axle.
(i) The flywheel is in translational equilibrium. Distinguish between translational
equilibrium and rotational equilibrium. ira)
(ii) At t=5.00s the flywheel is spinning with angular velocity 200rad s~. The support
bearings exert a constant frictional torque on the axle. The flywheel comes to
rest after 8,00 x 10° revolutions. Calculate the magnitude of the frictional torque
exerted on the flywheel. (3)
(Option B continues on the following page)
