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Figure 1 shows a spinning toy rotating about its axis.

The moment of inertia of the toy about its axis of rotation is 3.5 x 10-5 kg m². The toy is rotating with an initial angular speed of 19.4 rad s¹.A constant frictional torque of 2.7 x 104 N m acts on the toy.The toy decelerates to rest. Calculate the time taken for the toy to decelerate to rest. Three identical metal knobs are added to the rim of the toy as shown in Figure 2. The centre of mass of each knob is 4.6 cm from the axis of rotation.

The addition of the three knobs increases the moment of inertia of the toyto 8.1 x 105 kg m² about its axis of rotation. Calculate the mass of one knob. 3Figure 3 shows a force F of constant magnitude acting on one of the knobs to make the toy rotate again.

Facts for a time of 0.12 s in a direction tangential to the rim. The toy gains an angular momentum of 2.1 x 104 kg m² s ¹. The frictional torque is still 2.7 × 104 Nm. Calculate the magnitude of F.

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