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Question 19N.3.SL.TZ0.5b(ii)

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Date November 2019 Marks available [Maximum mark: 2] Reference code 19N.3.SL.TZ0.5b(ii)
Level SL Paper 3 Time zone TZ0
Command term Show that Question number b(ii) Adapted from N/A
b(ii).
[Maximum mark: 2]
19N.3.SL.TZ0.5b(ii)

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=12MR2.

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.

(b(ii))

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

[2]

Markscheme

use of L = lω = area under graph = 1.80 «kg m2 s–1» ✔

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

«to get ω = 200 rad s–1 »

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