Physics · Circular Motion & Momentum

The correct answer is Option A: Velocity is zero. When the velocity (v) of an object is zero, it signifies that the object is not moving, resulting in an angular displacement (θ) of zero, as described by the equation θ = ωt. Since angular velocity (ω) is defined as ω = v/r, if v is zero, then θ must also be zero.

Option B states that radial distance is zero, which means the object is at the axis of rotation, where linear velocity also becomes zero. However, this does not guarantee that angular displacement is zero unless the object is stationary at that point.

Option C incorrectly implies that both conditions (A and B) must be true simultaneously to achieve zero angular displacement, which is not accurate.

Option D incorrectly asserts that angular displacement can never be zero, which contradicts established principles of circular motion.

When the velocity (v) of an object is zero, it means that the object is not moving. Therefore, the angular displacement (θ) must also be zero, as there is no change in position over time. This can be derived from the equations θ = ωt and ω = v/r, where ω is angular velocity and r is the radial distance.

If the radial distance (r) is zero, the object is located at the axis of rotation. While this means that the linear velocity (v) is also zero, it does not directly imply that angular displacement (θ) is zero unless the object is also stationary. Thus, while this condition can lead to a zero angular displacement, it is not definitive on its own.

This option incorrectly suggests that both conditions individually guarantee zero angular displacement. While both can result in zero angular displacement, they do not both have to occur simultaneously; therefore, this option is misleading.

This option is incorrect because it asserts that angular displacement cannot be zero under any circumstances, which contradicts the principles of circular motion. Angular displacement can indeed be zero when either velocity is zero or radial distance is zero.