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McGill University
PHYS 101
Kenneth Ragan

Phys 101 Alanna Houston October 23, 2007 Rotational Motion - A point at a distance r moves through an arc of length L with: θ = L/r - Dealing mostly with radians! - Objects with the same angular velocity do not always move at the same speed. - 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 = 5m - 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
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