The angular position of a point on the rim of a rotating wheel is given by theta

ID: 1452074 • Letter: T

Question

The angular position of a point on the rim of a rotating wheel is given by theta=4.0t-3.0t^2+t^3, where theta is in radians and t is in seconds.

a) is the wheel ever stopped? If so, when?

b) When does the wheel have minimum angular velocity? Estimate the minimum angular velocity.

c) Is this rotation clockwise or counterclockwise?

d) In which time duration (between t=0 and t=5s) is the rotation speeding up?

e) Make a graph of the angular velocity in this rotation for the time between t=0s and t=5s

f) Make a graph of angular acceleration for the time between t=0s and t=5s

a) (t) = d/dt = d/dt (4.0t 3.0t^2 + t^3) = 4.0 6.0t + 3.0t^2 . solving this for 0 we get imaginary value of t.So wheel would never stop

b) it will have minimum or mximum angular velocity when d(t)/dt =0

= 6t-6 so at t=1 it will be max or min. since acceleration will be positive after t=1 so it will have minim angular velocity at t=1.

c) since the rotation is positive at t=0 it would be anti clock wise.

d) after t=1 it is spedding up.

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