A disc rotating about its axis with angular speed $\omega_0$ is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in will the disc roll in the direction indicated?
Exercise
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$\text{v}_{\text{A}}=\text{R}\omega_0,\text{ v}_\text{B}=\text{R}\omega_0,\text{ v}_\text{C}=\Big(\frac{\text{R}}{2}\Big)\omega_0$ The disc will not roll, Angular speed of the disc $=\omega_0$ Radius of the disc = R Using the relation for linear velocity, $\text{v}=\omega_0\text{R}$
For point A: $\text{v}_{\text{A}}=\text{R}\omega_0,$ in the direction tangential to the right. For point B: $\text{v}_{\text{B}}=\text{R}\omega_0,$ in the direction tangential to the left. For point C: $\Big(\frac{\text{R}}{2}\Big)\omega_0$ in the direction same as that of $v_A$. The directions of motion of points A, B, and C on the disc are shown in the following figure:
Since the disc is placed on a frictionless table, it will not roll. This is because the presence of friction is essential for the rolling of a body.
For point A: $\text{v}_{\text{A}}=\text{R}\omega_0,$ in the direction tangential to the right. For point B: $\text{v}_{\text{B}}=\text{R}\omega_0,$ in the direction tangential to the left. For point C: $\Big(\frac{\text{R}}{2}\Big)\omega_0$ in the direction same as that of $v_A$. The directions of motion of points A, B, and C on the disc are shown in the following figure:
Since the disc is placed on a frictionless table, it will not roll. This is because the presence of friction is essential for the rolling of a body.
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