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.
The back (small) sprocket of a bicycle has a radius r = 5 cm and the pedal sprocket has radius r = 12.5 cm. IF the pedal (sprocket) is rotated 100 rpm, what is the angular speed of the wheel?
Given data:
The small back sprocket of a bicycle has a radius: r1 = 5 cm
The pedal sprocket’s radius is: r2 = 12.5 cm
The rotation of the pedal sprocket is: N = 100 rpm
The angular speed of the pedal sprocket is: ω2
The angular speed of the wheel is: ω1
The angular speed of the pedal sprocket is calculated as,
The expression for linear speed is given as,
Here, v is the linear velocity of the bicycle, which is constant.
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