An exhausted bicyclist pedals somewhat erratically when exercising on a static bicycle. The angular velocity of...

An exhausted bicyclist pedals somewhat erratically when exercising on a static bicycle. The angular velocity of the wheels follows the equation ω(t)=at−bsin(ct)fort≥0, where t represents time (measured in seconds), a = 0.500 rad/s2 , b = 0.250 rad/s and c = 2.00 rad/s .

Part A

There is a spot of paint on the front wheel of the bicycle. Take the position of the spot at time t=0 to be at angle θ=0 radians with respect to an axis parallel to the ground (and perpendicular to the axis of rotation of the tire) and measure positive angles in the direction of the wheel's rotation. What angular displacement θ has the spot of paint undergone between time 0 and 2 seconds?

Part B

Express the angular displacement undergone by the spot of paint at t=2 seconds in degrees. Remember to use the unrounded value from Part A, should you need it.

Express your answer in degrees using three significant figures.

Part C

What distance d has the spot of paint moved in 2 seconds if the radius of the wheel is 50 centimeters?

Part D

Which one of the following statements describes the motion of the spot of paint at t=2.0 seconds?

Which one of the following statements describes the motion of the spot of paint at seconds?

	A)The angular acceleration of the spot of paint is constant and the magnitude of the angular speed is decreasing.
B)	The angular acceleration of the spot of paint is constant and the magnitude of the angular speed is increasing.
C)	The angular acceleration of the spot of paint is positive and the magnitude of the angular speed is decreasing.
D)	The angular acceleration of the spot of paint is positive and the magnitude of the angular speed is increasing.
E)	The angular acceleration of the spot of paint is negative and the magnitude of the angular speed is decreasing.
F)	The angular acceleration of the spot of paint is negative and the magnitude of the angular speed is increasing.

Expert Solution

genius_generous answered 38 minutes ago

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