Angular momentum L is given by L = Iω, thus ω = L/I.

The linear speed v of a point on the edge of the disc is given by v = Rω.

Angular momentum L = Iω, where I is the moment of inertia. If radius is doubled, I increases by a factor of 4, but ω decreases by a factor of 2, so L remains the same.

Kinetic energy of rotation is given by KE = (1/2)Iω². If ω is doubled, KE becomes (1/2)I(2ω)² = 4(1/2)Iω² = 4KE = 400 J.

Rotational kinetic energy K.E. = (1/2)Iω².

Rotational kinetic energy K = (1/2)Iω² = (1/2)(3 kg·m²)(10 rad/s)² = 150 J.

The rotational kinetic energy is given by KE = 0.5 I ω² = 0.5 * 3 * (4)² = 24 J.

The rotational kinetic energy is given by KE = (1/2)Iω² = (1/2)(5 kg·m²)(4 rad/s)² = 40 J.

L = Iω, if I is halved and ω is doubled, L' = (1/2)(2ω) = L.

Angular momentum L = Iω. If I is doubled and ω remains constant, L also doubles.

Using L = Iω, we find ω = L/I = 10/2 = 5 rad/s.

Using L = Iω, we have ω = L/I = 10 kg·m²/s / 2 kg·m² = 5 rad/s.

Angular momentum L = Iω, thus ω = L/I = 12 kg·m²/s / 4 kg·m² = 3 rad/s.

Angular momentum L = Iω, thus ω = L/I = 15 kg·m²/s / 3 kg·m² = 5 rad/s.

Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.

Angular momentum L = Iω; if I is doubled and ω remains constant, L remains the same.

New angular momentum L' = I'ω' = (1/2 I)(2ω) = Iω = L.

New angular momentum L' = I'ω' = (1/2I)(2ω) = L.

Rotational kinetic energy K = (1/2)Iω² = (1/2)(3 kg·m²)(30 rad/s)² = 450 J.

Angular deceleration = (final angular velocity - initial angular velocity) / time = (0 - 30 rad/s) / 5 s = -6 rad/s².

Angular momentum is conserved in the absence of external torque.

Using L = Iω, we have ω = L/I = 10/2 = 5 rad/s.

Angular momentum L = Iω, if ω is doubled, L becomes 2I(2ω) = 4L.

Angular momentum L = Iω; if ω is doubled, L becomes 2I(2ω) = 4L.

Angular momentum L is proportional to angular velocity, so if angular velocity is doubled, angular momentum becomes 4L.

Average velocity = total distance / total time = 400 m / 50 s = 8 m/s.

Average speed = Total distance / Total time = 400 m / 50 s = 8 m/s.

Average velocity = total displacement / total time. Since the runner returns to the starting point, displacement = 0. Average velocity = 0 m / 50 s = 0 m/s.

Average velocity = total displacement / total time. Since the runner returns to the starting point, displacement = 0. Average velocity = 0 m/s.

Speed = Distance/Time = 400 m/50 s = 8 m/s