A child is outside his home playing with a metal hoop and stick. He uses the stick to keep the hoop of radius 45.0 cm rotating along the road surface. At one point the hoop coasts downhill and picks up speed. (a) If the hoop starts from rest at the top of the hill and reaches a linear speed of 9.40 m/s in 14.5 s, what is the angular acceleration, in rad/s2, of the hoop?  rad/s2 (b) If the radius of the hoop were larger, how would this affect the angular acceleration of the hoop? The angular acceleration would decrease. The angular acceleration would increase.     There would be no change to the angular acceleration.

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Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.