IB Physics HL A 4 5 Hl Angular Motion Equations Questions

Apply rotational SUVAT equations to angular speed, acceleration, displacement, revolutions and stopping time when angular acceleration is uniform.

Exam points

Select and apply the appropriate rotational SUVAT equation to calculate angular speed, acceleration, displacement or time when angular acceleration is uniform.
Convert angular displacement between radians and revolutions when finding rotations, stopping distance or travel during a kinematics calculation.
Combine rotational kinematics with τ/I and linear–angular conversions in multi-step rotating-system problems.
Explain why a constant-angular-acceleration equation cannot be used when the torque, and therefore angular acceleration, changes.

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Study A.4.5 (HL)—Angular motion equations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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A horizontal rigid bar of length 2 R is pivoted at its centre. The bar is free to rotate in a horizontal plane about a vertical axis through the pivot. A point particle of mass M is attached to one end of the bar and a container is attached to the other end of the bar.

A point particle of mass $\frac{M}{3}$ moving with speed v at right angles to the rod collides with the container and gets stuck in the container. The system then starts to rotate about the vertical axis.

The mass of the rod and the container can be neglected.

Figure for Question IB Physics HL A 4 5 Hl Angular Motion Equations Questions question 1 — IB Physics HL

A torque of 0.010 Nm brings the system to rest after a number of revolutions. For this case $R=0.50 \mathrm{~m}, M=0.70 \mathrm{~kg}$ and $v=2.1 \mathrm{~ms}^{-1}$ .

Calculate the number of revolutions made by the system before it comes to rest.

$\theta=\frac{\omega_i^{2}}{2\alpha}$ , from $\omega_f^{2}=\omega_i^{2}+2\alpha\theta$ $\theta=\frac{v^{2}}{32R^{2}\alpha}=\frac{2.1^{2}}{32\times0.5^{2}\times0.043}=12.8\text{ or }12.9\ \mathrm{rad}$
number of rotations $=\frac{12.9}{2\pi}=2.0$ revolutions

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IB Physics HL A 4 5 Hl Angular Motion Equations Questions question 1