Physics · System Of Particles And Rotational Motion · NEET
Yes. This is the key idea. When a rigid body rotates about a fixed axis, every particle sweeps the same angle in the same time, so ω is identical for all points. What changes from point to point is the linear velocity v = rω, because r (distance from the axis) is different for each particle. The rim of a wheel moves fast; a point near the axle moves slowly, even though both share one ω.
Think about the definition. In one full turn the particle covers a circle of circumference 2πr in time T. So v = 2πr / T. Also ω = 2π / T. Divide: v / ω = r, which gives v = rω. A bigger r or a bigger ω both make the particle move faster, so both multiply. If it were r/ω, faster spinning would give slower motion, which is wrong.
Angular velocity ω tells how fast the angle changes (unit: rad/s) and is the same for the whole body. Linear velocity v tells how fast a particle actually moves along its circular path (unit: m/s) and is tangent to the circle. They are linked by v = rω. So ω describes the rotation as a whole; v describes the motion of one specific particle at distance r.
Yes. A particle lying exactly on the rotation axis has r = 0, so v = rω = 0. It only spins in place. This is why the centre of a rotating wheel (on the axle) stays put while the rim races around. The velocity grows linearly as you move outward from the axis.
r is the perpendicular distance from the axis of rotation to the particle, not necessarily from a chosen centre point. For a flat disc rotating about a perpendicular axis through its centre, this equals the distance from the centre. But in general (a 3D body), always use the shortest distance to the axis line.
Yes, they are identical because multiplication order does not matter for the magnitudes: rω = ωr. Both give the speed in m/s when ω is in rad/s and r in metres. Just remember ω must be in radians per second, not rpm, before you plug in.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
v = rω, where v is linear (tangential) speed in m/s, r is the perpendicular distance from the axis in metres, and ω is angular velocity in rad/s. In vector form v = ω × r.
v is in m/s, r is in metres, and ω is in radians per second. Radian is dimensionless, so rad/s × m gives m/s correctly.
The point farthest from the axis, because v = rω and ω is common to all points. So the largest r gives the largest v.
It is tangent to the circular path at that instant, perpendicular to the radius. The vector relation v = ω × r fixes both magnitude and direction.
Use ω = 2πN/60 rad/s, where N is revolutions per minute. Then apply v = rω. For example, 300 rpm gives ω = 2π × 300 / 60 = 10π rad/s.
