Motion in a Circle

 Motion in a Circle
Kinematics of uniform circular motion
Radian (rad) is the S.I. unit for angle, θ and it can be related to degrees in the following way. In one complete revolution, an object rotates through 360° , or 2π rad.
As the object moves through an angle θ, with respect to the centre of rotation, this angle θ is known as the angular displacement.
Angular velocity (ω) of the object is the rate of change of angular displacement with respect to time.
ω = θ / t = 2π / T (for one complete revolution)
Linear velocity, v, of an object is its instantaneous velocity at any point in its circular path.
v = arc length / time taken = rθ / t = rω
  • The direction of the linear velocity is at a tangent to the circle described at that point. Hence it is sometimes referred to as the tangential velocity
  • ω is the same for every point in the rotating object, but the linear velocity v is greater for points further from the axis.
A body moving in a circle at a constant speed changes velocity {since its direction changes}. Thus, it always experiences an acceleration, a force and a change in momentum.
Centripetal acceleration
a = rω2 = v2 / r {in magnitude}
Centripetal force
Centripetal force is the resultant of all the forces that act on a system in circular motion.
{It is not a particular force; “centripetal” means “centre-seeking”. Also, when asked to draw a diagram showing all the forces that act on a system in circular motion, it is wrong to include a force that is labelled as “centripetal force”. }
Centripetal force, F = m r ω 2 = mv2 / r {in magnitude}
A person in a satellite orbiting the Earth experiences “weightlessness” although the gravi field strength at that height is not zero because the person and the satellite would both have the same acceleration; hence the contact force between man &
satellite / normal reaction on the person is zero {Not because the field strength is negligible}.


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