Circular Motion

• • Explain why an object moving at constant speed in a circle is accelerating?

  As the object is moving at constant speed, it is also changing direction so the velocity is changing. Since acceleration= (change) velocity over(change) time. The Object must be accelerating.
• • Explain why no work is done on the object

  Because the centripetal force acts perpendicular to the velocity vector there is no motion in the direction of the force meaning no work is therefore done.
• For a particle moving in a circle of uniform speed, which one of the following statements is correct?, A. The kinetic energy of the particle is constant. B. The force on the particle is the same direction of motion of the particle. C. The momentum of the particle is constant. D. The displacement of the particle is in the direction of the force.

  A. The kinetic energy of the particle is constant
• When a particle of mass m is moving in a circle of radius r at uniform speed, taking time for each revolution. The kinetic energy of the particle is: $(π^2mr^2)/T^2$
• A mass on the end of a string is whirled round in a horizontal circle at increasing speed until the string breaks. The subsequent path taken by the mass is a parabola in a vertical plane.
• A particle of mass m moves in a circle of radius r at uniform speed with frequency f. The kinetic energy of the particle is : $2π^2mf^2r^2$
• A particle travels at a constant speed around a circle of radius r with centripetal acceleration. What is the time taken for ten complete rotations?

  $20π√(r/a)$
• A satellite of mass m travels in a circular orbit of radius r around a planet of mass M. What expression gives the angular speed of the satellite?

  $√(GM/r^3)$
• Circular measure: Angular measurements in circular motion are usually made in the SI unit the radian.
• One radian is the angle subtended at the centre of a circle by an arc of length equal to the radius of the circle.
• Angular speed or angular frequency, 𝝎, is the rate of change of angular displacement
• For one complete revolution: $v=$$2πr/T$
• The velocity vector of the object is along the tangent to that point on its path.
• Centripetal acceleration: $a=$$w^2r$
• Centripetal Force:$F=$$mw^2r$
• The centripetal force on the clothes is provided by the normal contact force acting on the clothing from the drum surface
• The angular speed of the drum is the same at all points along the radius of the drum.
• The velocity of the clothing is constantly changing.
• The acceleration of an object moving with simple harmonic motion is zero when the object moves through the centre of the oscillation.
• The bob of a simple pendulum moves with undamped simple harmonic motion - the total energy of the bob is constant.