Question

If a point moves along a circle with constant speed, prove that its angular speed about any point on the circle is half of that about the centre.

Answer 1

•IF A POINT MOVES ALONG A CIRVLE WITH CONSTANT SPEED, THEN ITS ANGULAR SPEED ABOUT ANY POINT ON THE CIRCLE IS HALF OF THAT ABOUT THE CENTRE.

•We consider the movement of the PARTICLE ABOUT THE CENTRE, Let the PARTICLE be at any position on the CIRCLE at any time t.

•Now we use the formula of ANGULAR VELOCITY

W0= dx/dt

Wc= d(2x)/dt = 2dx/dt

• Wc = 2W0

Answer 2

A point is moving along a circle which means it will have the angular velocity.

• Let the angular velocity of the particle is denoted by ω=dФ/dt
• Ф is the angle formed by the point while circular motion.
• Let P be the point
• O be the center of circle.
• As the particle moving at some other point the angle at that time be 2Ф
• Therefore the angular velocity at that ω₁=d(2Ф)/dt
• ω₁=2dФ/dt
• From the above the equation
• w=2w₁
• Hence the angular velocity is twice at the center to any other point.