Question

A particle moves along a circle of radius r with uniform speed v. The angle described by the particle in one second is:

(a) v/r

(b) r/v

(c) v

(d) r

Answer 1

The angle described by a particle moving in a circle with uniform speed v and radius r, in one second, is v/r radians. This is determined by the relationship between linear speed, radius, and angular velocity.

Step-by-step explanation:

To determine the angle described by a particle moving in a circle with uniform speed, we need to consider the relationship between linear speed (v), radius (r), and angular velocity (ω). The speed of the particle provides a way to find the distance it travels in a given time, and applying the formula for circumference (2πr) allows us to calculate the total distance traveled in one revolution.

The angular velocity of the particle is given by ω = v/r. The particle describes an angle in radians equal to the angular velocity times the time. Therefore, in one second, the particle describes an angle Δθ = ω * (1 s) = v/r * 1 = v/r radians since angular velocity is measured in radians per second.

In the case where the particle is a charged particle moving perpendicular to a magnetic field, the same logic applies even though additional forces are acting on the particle. The radius given in these problems typically represents the uniform circular motion that the particle undergoes due to the Lorentz force, and doesn’t affect the calculation of the angle described per second if the speed is constant.