Question

The speed  of a circular table is doubled and it's angular velocity is halved what happens to centripetal force?
1. Becomes thrice
2. Remains same
3. Halved
4. Doubled

Answer 1

Correct Answer - Option 2 : Remains same

CONCEPT:

• Circular motion: It is a movement of an object along the circumference of a circle or rotation along a circular path.
  • It can be uniform, with the constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation.
  • Some of the most common examples of circular motion include: 
  1. The man-made satellite that revolves around the earth
  2. A rotating ceiling fan, a moving car’s wheel
  3. The blades in a windmill, and gears in gas turbines.
  • ​The acceleration of a particle in a circular motion is always directed towards the center.
  • And the centripetal force acting towards the center is given by:

Formula:

acceleration (a) = v2/r 

Relation between linear and angular velocity is :

v = r ω 

where, a = acceleration (m/s²), v = linear velocity  (m/s), r = radius (m), ω = angular velocity

CALCULATION:

Given that, v₂ = 2v₁, ω₂ = 1/2 ω₁

where, v2 = final velocity,v₁ = initial velocity, ω2 =final angular velocity, ω₁ = intial angular velocity.

As we know the linear velocity,

v = rω ,

Centripetal acceleration (a)= v²/r = ω v

a₁ = a₂

ω₁ v₁ = ω₂ r₂ = 1/2 ω₁v₂ = ω₁v₁

From above its clear that it remains unchanged.

The correct option is 2.