IB DP Physics Topic 2: Mechanics Question Bank SL Paper 3

Question

A wheel of mass 0.25 kg consists of a cylinder mounted on a central shaft. The shaft has a radius of 1.2 cm and the cylinder has a radius of 4.0 cm. The shaft rests on two rails with the cylinder able to spin freely between the rails.

The stationary wheel is released from rest and rolls down a slope with the shaft rolling on the rails without slipping from point A to point B.

The wheel leaves the rails at point B and travels along the flat track to point C. For a short time the wheel slips and a frictional force F exists on the edge of the wheel as shown.

a.i.

The moment of inertia of the wheel is 1.3 × 10–4 kg m2. Outline what is meant by the moment of inertia.

[1]
a.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.

[3]
a.iii.

Determine the angular velocity of the wheel at B.

[1]
b.i.

Describe the effect of F on the linear speed of the wheel.

[2]
b.ii

Describe the effect of F on the angular speed of the wheel.

[2]

Markscheme

a.i.

an object’s resistance to change in rotational motion

OR

equivalent of mass in rotational equations

OWTTE

[1 mark]

a.ii.

ΔKE + Δrotational KE = ΔGPE

OR

$$\frac{1}{2}$$mv2 + $$\frac{1}{2}$$I$$\frac{{{v^2}}}{{{r^2}}}$$ = mgh

$$\frac{1}{2}$$ × 0.250 × v2 + $$\frac{1}{2}$$ × 1.3 × 10–4 × $$\frac{{{v^2}}}{{1.44 \times {{10}^{ – 4}}}}$$ = 0.250 × 9.81 × 0.36

v = 1.2 «m s–1»

[3 marks]

a.iii.

ω «= $$\frac{{1.2}}{{0.012}}$$» = 100 «rad s–1»

[1 mark]

b.i.

force in direction of motion

so linear speed increases

[2 marks]

b.ii

force gives rise to anticlockwise/opposing torque on

wheel ✓ so angular speed decreases ✓

OWTTE

[2 marks]