Exams › NEET › Physics

A particle moves in a circular path. If \(\omega\) is the angular velocity vector and \(\vec r\) is the position vector of the particle from the centre, which expression correctly gives the linear velocity \(\vec v\) of the particle?

1. \(\vec v = \vec r \cdot \omega\)
2. \(\vec v = \omega \cdot \vec r\)
3. \(\vec v = \omega \times \vec r\)
4. \(\vec v = \vec r / \omega\)

Correct answer: \(\vec v = \omega \times \vec r\)

Solution

For a particle in circular motion, the instantaneous linear velocity is given by the cross product of angular velocity and position vector. This ensures the velocity is tangential to the path and perpendicular to the radius vector.

Related NEET Physics questions

• A stone tied to a string of length 80 cm is whirled in a horizontal circle at constant speed, completing 14 revolutions in 25 s. What is the magnitude of the centripetal acceleration of the stone?
• A coin on a rotating turntable begins to slip when placed 4 cm from the center. If the turntable's angular speed is doubled, at what distance from the center will the coin just start to slip?
• The angular displacement of a rotating body is described by $\theta(t) = \omega_0 t + \frac{1}{2}\alpha t^2$, where $\omega_0 = 1\ \text{rad/s}$ and $\alpha = 1.5\ \text{rad/s}^2$. What is the angular velocity of the body at $t = 2\ \text{s}$?
• A coin rests on a gramophone record rotating at angular velocity \(\omega\). The coefficient of static friction is \(\mu\). The coin rotates without slipping if its distance \(r\) from the center satisfies:
• Two racing cars of masses \(m_1\) and \(m_2\) travel in circles of radii \(r_1\) and \(r_2\), respectively. Both complete one full revolution in the same time period \(t\). What is the ratio of the angular speed of the first car to the second car?
• A wheel starts from rest and undergoes uniform angular acceleration, reaching an angular velocity of 80 rad/s after 5 seconds. What is the total angular displacement of the wheel during this time?

⚔️ Practice NEET Physics free + battle 1v1 →