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Which of the following is the most accurate example of uniform circular motion in daily life?
A car speeding up on a curved road
A ceiling fan blade rotating at a constant speed
A stone thrown into the air
A train moving on a straight track
A ceiling fan blade rotating at a constant speed
Uniform Circular Motion (UCM) is the motion of an object moving at a constant speed along a circular path. In this state, the speed remains constant, but the velocity changes continuously due to the constant change in the direction of motion.
Uniform Circular Motion (UCM) is the motion of an object moving at a constant speed along a circular path. In this state, the speed remains constant, but the velocity changes continuously due to the constant change in the direction of motion.
Think of a clock's second hand or a merry-go-round moving at a steady pace; even though you aren't going faster, your body is constantly 'turning' to stay in the circle.
UCM: Uniform (Speed) Constant (Motion in Circle).
v=╧Йr тАФ Relationship between linear velocity v, angular velocity ╧Й, and radius r
acтАЛ=rv2тАЛ тАФ Centripetal acceleration acting towards the center
T=╧Й2╧АтАЛ тАФ Period of one complete rotation
In UCM, the magnitude of velocity (speed) is v=T2╧АrтАЛ, where r is the radius and T is the period. Because the direction of velocity is always tangential to the circle, a centripetal force FcтАЛ=rmv2тАЛ directed toward the center is required to maintain the circular trajectory. A ceiling fan achieves this as its blades rotate at a steady angular velocity ╧Й, where v=r╧Й.
In UCM, speed is constant but velocity is variable.
Acceleration in UCM is centripetal acceleration, which is perpendicular to the velocity vector.
No work is done by the centripetal force as displacement is always perpendicular to the force.
The angular velocity ╧Й remains constant for the entire rotating body.
Provides predictable and stable motion patterns for mechanical systems.
Requires constant inward force, which can cause wear and tear on components like motor bearings.
Ceiling and table fans
Satellite motion in geostationary orbit
Option A is incorrect because 'speeding up' implies non-uniform circular motion (tangential acceleration exists).
Option C is projectile motion, which follows a parabolic trajectory, not a circular one.
Option D is linear motion, where the direction of velocity remains constant.
B is correct тАФ A ceiling fan blade rotating at a constant speed maintains a constant radius and constant angular velocity, satisfying all criteria for uniform circular motion.
Always remember that in circular motion, the object is technically 'accelerating' because velocity is a vector; since the direction changes, the velocity changes, thus implying acceleration.