Question 19N.3.SL.TZ0.b(ii)
| Date | November 2019 | Marks available | [Maximum mark: 2] | Reference code | 19N.3.SL.TZ0.b(ii) |
| Level | SL | Paper | 3 | Time zone | TZ0 |
| Command term | Show that | Question number | b(ii) | Adapted from | N/A |
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 .
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.
Show that the angular velocity of the flywheel at t = 5.00 s is 200 rad s–1.
[2]
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 »
