IB Physics HL A 4 4 Hl Angular Motion Quantities Questions

Convert between linear and angular displacement, speed and acceleration, and use radius and rotation data to solve rotational-motion problems.

Exam points

Convert linear displacement, speed and tangential acceleration to angular quantities using the radius, retaining radian units.
Calculate angular velocity or angular acceleration from rotational speed, linear motion and elapsed time.
Determine angular displacement from revolutions, arc length or an angular-displacement/time graph.
Use angular displacement and angular speed to calculate the time for a body to complete part of a rotation.

Learn this topic

Study A.4.4 (HL)—Angular motion quantities conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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.

All question bank results loaded

Learn this topic

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

Question (a)

Question (i)

Question (b)

Question (i)

Question (ii)