The electric field E between the plates of a parallel plate capacitor is given by E = V/d, where d is the separation between the plates.

Maximum speed (v_max) = ωA. Thus, ω = v_max/A = 4/2 = 2 rad/s.

The third force can be determined by vector addition of the first two forces to ensure the net force is zero.

The tangential speed v is given by v = rω.

The tangential speed v is given by v = rω.

Centripetal acceleration a_c = v²/R.

L = mvr = 4 kg * 3 m/s * 2 m = 24 kg·m²/s.

Angular momentum L = mvr, if v is doubled, L also doubles.

The angular momentum is constant because the particle's velocity and distance from the point are constant.

Angular momentum L = mvr, where v is the linear speed and r is the radius of the circular path.

Angular momentum L = mvr, where r is the perpendicular distance from the line of motion to point O.

Using the equation v = u + at, where u = 3 m/s, a = 2 m/s², and t = 5 s, we get v = 3 + (2 * 5) = 3 + 10 = 13 m/s.

Angular velocity ω = v/r = 6 m/s / 3 m = 2 rad/s.

Centripetal acceleration (a_c) = v²/r = (5²)/10 = 2.5 m/s².

Circumference = 2πr = 20π m. Period T = distance/speed = 20π m / 5 m/s = 4π s.

Period T = (2πr)/v = (2π * 10)/5 = 4π s.

Period T = (2πr)/v = (2π * 10)/5 = 4π s.

Time period T = 2πr/v = 2π(10 m) / (5 m/s) = 4π s.

Centripetal acceleration (a_c) = v²/r = (10 m/s)² / (5 m) = 20 m/s².

Angular displacement θ = 0.5αt² for constant angular acceleration.

The time period T = 2π/ω for uniform circular motion.

Centripetal acceleration a_c = v^2/R.

Centripetal force F = mv^2/r.

Angular velocity (ω) = v/r = 10/2 = 5 rad/s.

The particle has centripetal acceleration directed towards the center of the circle.

Linear speed (v) = Circumference / Time = (2π * 10 m) / 5 s = 4π m/s.

Circumference = 2πr = 20π m. Time = distance/speed = 20π m / 5 m/s = 4π s.

Time period (T) = (2πr)/v = (2π * 10)/5 = 4π s.

Linear speed (v) = 2πr/T = 2π(15 m)/10 s = 3 m/s.

Circumference = 2πr = 2π(2) = 4π m. Speed = Distance/Time = 4π/4 = π m/s ≈ 3.14 m/s.