Angular Velocity — Prelims Questions

A particle moves in a circle of radius $50$ cm with a constant angular velocity. If it completes $10$ revolutions in $5$ seconds, what is its angular velocity in rad/s?

A wheel of radius $0.5$ m is rotating with an angular velocity of $120$ rpm. What is the linear speed of a point on its rim?

Two particles A and B are on a rotating disc. Particle A is at a distance $R$ from the center, and particle B is at a distance $2R$ from the center. Which of the following statements is true regarding their angular and linear velocities?

A particle starts from rest and undergoes angular acceleration $\alpha = 2t$ rad/s$^2$. What is its instantaneous angular velocity at $t=2$ s?

A point on the rim of a wheel has a linear speed of $10$ m/s. If the radius of the wheel is $0.2$ m, what is the angular velocity of the wheel?

A rigid body rotates about the z-axis. If the rotation is clockwise when viewed from the positive z-axis, what is the direction of its angular velocity vector?