1) A wheel with a radius of 5 m is spinning with an angular velocity of +40 rad/

Question

1) A wheel with a radius of 5 m is spinning with an angular velocity of +40 rad/s. a) What is the period of rotation? b) What is the magnitude of the tangent velocity? c) What is the magnitude of the centripetal acceleration? 2) The wheel from the previous problem comes to a stop with constant angular acceleration over an angle of 200 rad. a) Solve for the angular acceleration symbolically based on the given quantites (do not substitute in any values, including 0 values). b) What is the angular acceleration (numerically)? c) What is the magnitude of the tangent acceleration (numerically)?

Explanation / Answer

1) radius r = 5m
angular speed, w = 40 rad/s

a. time period of rotation T = 2*pi/w = 2*pi/40 = 0.157 s
b. atngent veocity v = wr = 40*5 = 200 m/s
c. centripital acceleration = w^2*r = 1600*5 = 8000 m/s/s

2) acceleration, a
angle, phi = 200 rad

a) 2*a*phi = w^2 - 0^2
a = (w^2 - 0^2)/2*phi

b) a = (1600)/2*200 = 4 rad/s/s
c) tangential acceleration = a*r = 20 m/s/s

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