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Angular to Linear Movements

Angular to Linear Movements. Linear velocity (v) can be determined using angular velocity ( w ) and arclength (s) calculations. There are two methods: Calculate the angular velocity in rad/sec and multiply by the radius OR Calculate the arclength and divide by time.  q. r.

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Angular to Linear Movements

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  1. Angular to Linear Movements Linear velocity (v) can be determined using angular velocity (w) and arclength (s) calculations. There are two methods: Calculate the angular velocity in rad/sec and multiply by the radius OR Calculate the arclength and divide by time

  2. q r General Example Basic Situation An object moves through a circular path with a radius r. The angle through which it moves is q0, and it makes this movement over time interval t. Calculate the linear velocity of the object.

  3. Angular to Linear Velocity Solution • Calculate the angular velocity • = q/t deg/sec • Convert w from deg/sec to rad/sec (w deg/sec)(1 rad /57.3 deg) = w rad/sec • Multiply angular velocity in rad/sec by the radius of the curve (w rad/sec)(r) = v

  4. ArclengthSolution • Convert the angle from deg to rad (q0)(1 rad/57.3 deg) = q rad • Calculate the arclength (s) s = (r)(q rad) • Divide the arclength by the time interval s/t = v

  5. q r EXAMPLE q = 800 r = 10 cm t = 5 sec

  6. Angular to Linear Velocity Solution • w = 80 deg/5 sec = 16 deg/sec • (16 deg/sec)(1 rad/57.3 deg) = .279 rad/sec • v = (.279 rad/sec)(10 cm) = 2.79 cm/sec

  7. Arclength Solution • (80 deg)(1 rad/57.3 deg) = 1.396 rad • s = (1.396 rad)(10 cm) = 13.96 cm • v = (13.96 cm)/(5 sec) = 2.79 cm/sec

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