Angular Mechanics - Radians Full circle: 360o = 2 Radians  = s/r Radians = m/m = ? r s 

Convert 14.0 rotations to radians: Angle Conversions: 1 rev = 1 rot = 2π rad = 360 deg Convert 14.0 rotations to radians: 88.0 rad

Convert 120. radians to rotations: Angle Conversions: 1 rev = 1 rot = 2π rad = 360 deg Convert 120. radians to rotations: 19.1 rot

Convert 170. degrees to radians: Angle Conversions: 1 rev = 1 rot = 2π rad = 360 deg Convert 170. degrees to radians: 2.97 rad

Convert 1.5708 radians into degrees: Angle Conversions: 1 rev = 1 rot = 2π rad = 360 deg Convert 1.5708 radians into degrees: 90.0 degrees

 = Δθ/t (omega is in rad/s, rot/s, and RPM) Angular velocity:  = Δθ/t (omega is in rad/s, rot/s, and RPM) 1 rev = 1 rot = 2π rad = 360 deg 1 minute = 60 seconds RPM = rev/min

Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg 1 minute = 60 seconds Convert 15.0 rot/s to rad/s: 94.2 rad/s

Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg 1 minute = 60 seconds Convert 67.0 rad/s to rot/s: 10.7 rot/s

Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg 1 minute = 60 seconds Convert 78.0 RPM to rad/s: 8.17 rad/s

Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg 1 minute = 60 seconds Convert 12.2 rad/s to RPM: 117 RPM

Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg 1 minute = 60 seconds Convert 3.20 rot/s to RPM 192 RPM

Angular Velocity Conversions: 1 rev = 1 rot = 2π rad = 360 deg 1 minute = 60 seconds Convert 45 RPM to rot/s 0.750 rot/s

Angular Mechanics - Tangential Relationships Linear: (m) s (m/s) v (m/s/s) a Tangential: (at the edge of the wheel) = r - Displacement* = r - Velocity = r - Acceleration* *Not in data packet

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A 68.0 cm diameter car tire rolls through 16.0 radians. What distance does the car travel? 5.44 m

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A 41.0 cm radius bike tire rolls 50.0 m. Through what angle in radians does the tire rotate? 122 radians

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A 0.320 m radius tire is rotating at 230. rad/s. What is the lineal speed at the edge of the wheel? 73.6 m/s

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A 1.60 m diameter aircraft landing wheel strikes the ground at 54.0 m/s. What is the angular velocity of the wheel? 67.5 rad/s

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A skateboard with 52.0 mm wheels that are accelerating angularly at 120. rad/s/s has what linear acceleration? (52.0 mm is the diameter) 3.12 m/s/s

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A skateboard with 64.0 mm (diameter) wheels accelerates at 4.50 m/s/s. What is the angular acceleration of the skateboard? 141 rad/s/s

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A 78.0 cm diameter wheel rolls through 23.0 rotations. What lineal distance does it travel? 56.4 m

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A skateboard with 64.0 mm (diameter) rolls 100. m. Through how many rotations do the wheels rotate? 497 rotations

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A 0.340 m radius grinding wheel rotates at 750. RPM. What is the lineal speed at its edge? 26.7 m/s

s = θr, v = r, a = r Tangential Relationships: r is radius in m, and you must be in radians!!!!! A pitching machine uses 1.20 m diameter rotating wheels. What is their speed in RPM if it is pitching at 41.0 m/s? 653 RPM