Phys 101 Alanna Houston
October 23, 2007
- A point at a distance r moves through an arc of length L with: θ =
- Dealing mostly with radians!
- Objects with the same angular velocity do not always move at the
- In , theta is in radians. Radians are useful when angles
are very small since we then have: sin(θ) = x/r = L/r = θ, sin(θ) =
θ, tan(θ) = θ
- The human eye can distinguish an object that subtends an angle
of ~ 5x10^-4 rads. What is the minimum spatial extent that can
be distinguished at 1 km distance? (To subtend an angle means to
have that angular size)
- small theta therefore theta is the ratio of x/r, x = 5x10^-4 * 1km
- The angle theta is the equivalent of displacement x; the
equivalent of the velocity v is then the angular velocity ω.
- All points on the rigid body rotate at the same rate ω or frequency
- Similarly, angular acceleration will be
- Example: A hard disk spins at 15000 rpm. If the disk has a
diameter of 3”, what is the linear velocity at the edge of the disk?
o 1 inch = 2.54 cm, therefore r = 7.62/2 = 0.038 m
o v = ωr = (15000*2π/60) * 0.038 m = 60 m/s = 200 km/h Phys 101 Alanna Houston
- atan= αr
- If we have constant angular acceleration (α), the kinematics are
exactly analogous to those for constant linear acceleration but