IB Physics HL A.4.4 Angular motion quantities

[Maximum number: 3]

A boat is moved from land to water by rolling it across a set of cylindrical airbags.

Figure for Question IB Physics HL A 4 4 Hl Angular Motion Quantities Questions question 1 — IB Physics HL

(a)

Another way to move a boat down a ramp is to place it on rigid rods. Assume that the same boat is now moved on rods of diameter 1.80 m with the same boat acceleration as before.

[ 1 ]

(i)

Show that the angular displacement of a rod during the first 8.0 s of the motion is about 8 rad.

[ 1 ]

$\theta=2 \pi$ revolutions $=2 \pi \frac{s}{2 \pi r}=\frac{7}{0.9}=7.78 \mathrm{rad}$

(b)

During the testing of the rod, it is rotated about its central axis. Point P is on the surface of the rod. At time t=0, P is at a point $45^{\circ}$ above the horizontal. The linear speed of P is $2.0 \mathrm{~ms}^{-1}$ .

The vertical displacement x of P can be modelled with an equation $x=x_{0} \sin (\omega t+\phi)$ .

[ 2 ]

(i)

Calculate the angular velocity $\omega$ of P.

[ 1 ]

$\omega=\frac{v}{r}=\frac{2}{0.9}=2.22 \mathrm{rads}^{-1}$

(ii)

Calculate the time it will take for P to reach the top of the circle.

[ 1 ]

Alternative 1
$t=\frac{\left(\frac{\mathrm{C}}{8}\right)}{v}=\frac{\left(\frac{2 \pi \mathrm{r}}{8}\right)}{2.0}=0.35 \mathrm{~s}$

Alternative 2
$t=\frac{\left(\frac{\pi}{4}\right)}{\omega}=0.35 \mathrm{~s}$

Allow 0.35-0.36 s.

IB Physics HL A 4 4 Hl Angular Motion Quantities Questions question 1

Question (a)

Question (i)

Question (b)

Question (i)

Question (ii)