A particle moves  with constant angular velocity ω round the curve with polar equation  r=a(1-4sinθ), a>0 Find  i)The maximum speed of the particles and the polar coordinates of the point at which the speed is maximum ii)The tranverse component of the acceleration of the particles

There are more than 300 species of hummingbirds in the world and about 10 species regularly breed in the United States. One of which is the Ruby-throated Hmmingbird who can flap its wings with an angular speed of 332 rad/s. Calculate the period of its flapping motion.

The Earth orbits the Sun in a near circular orbit of radius 1.5 × 1011m. Find themagnitude of Earth’s velocity, angular velocity, and circular acceleration as itorbits the Sun. Hint: You already know the period of this orbit.  A car starts from rest on a curve with a radius of 120 m and acceleratedtangentially at a constant 1.0 Τm s2. Through what angle will the car havetravelled when the magnitude of its total acceleration is 2.0 m/s2?

The good expert Hand written solution is not allowed.

A bicycle tire is 66 cm in diameter. (a) At what frequency f does the tire rotate when the bicycle is traveling at a speed of 35 km/h? (b) What is the angular frequency ω?