Uniform Circular Motion: For sphere with a rotation angle of 2pi rad and 1 revolution what is a) angular speed b) linear speed c) radial acceleration
To find the angular speed (ω) of an object in uniform circular motion, we can use the formula:
ω = Δθ / Δt
Where Δθ is the change in the rotation angle and Δt is the time taken for that change. In this case, the rotation angle is given as 2π rad, which is equivalent to one complete revolution (360 degrees).
a) Angular Speed:
We know that 1 revolution is equal to 2π radians, and if the change in rotation angle is 2π rad, then the angular speed is:
ω = 2π rad / 1 revolution = 2π rad / 2π rad = 1 rad/rev
So, the angular speed is 1 radian per revolution.
b) Linear Speed:
The linear speed (v) of an object in uniform circular motion can be found by multiplying the angular speed (ω) by the radius (r) of the circular path.
v = ω * r
Since the radius is not provided in the question, we cannot determine the linear speed without that information.
c) Radial Acceleration:
The radial acceleration (ar) of an object in uniform circular motion can be found using the formula:
ar = ω^2 * r
Again, without the given radius (r), we cannot determine the radial acceleration.
In summary:
a) The angular speed is 1 rad/rev.
b) The linear speed cannot be determined without the radius.
c) The radial acceleration cannot be determined without the radius.