Question: A toy airplane hangs from the ceiling at the bottom end of a string. You turn the airplane many times to wind up the string clockwise and release it. The airplane starts to spin counter clockwise, slowly at first and then faster and faster. Take counter clockwise as the positive sense and assume friction is negligible. When the string is entirely unwound, the airplane has its maximum rate of rotation. (i) At this moment, is its angular acceleration (a) positive, (b) negative, or (c) zero? (ii) The airplane continues to spin, winding the string counter clockwise as it slows down. At the moment it momentarily stops, is its angular acceleration (a) positive, (b) negative, or (c) zero?
(i) The angular acceleration of an airplane, when it has maximum rate of rotation, is zero. Hence, option (c) is correct answer.
(ii) The angular acceleration of an airplane, when it winds the string counter clockwise as it slows down is negative. Hence, option (b) is correct answer.
Angular acceleration is defined as the time rate of change of angular velocity. It is calculated by using the formula given below:
Here is change in angular velocity and is change in time.
Given that counter clockwise direction should be taken positive and clockwise direction as negative. At maximum rate of rotation, change in angular velocity is zero because at maximum rate of rotation, initial and final velocities are same for a small interval . Hence, put , we get
Thus, angular acceleration of an airplane is zero when it has maximum rate of rotation. Hence, option(c) is the correct answer.
Though the angular speed is zero at the given instant, there is angular acceleration since the wound-up string applies a torque on the airplane. It is similar to the ball which is thrown upwards. At the top of its flight, it momentarily comes to rest, but is still accelerating because of the gravitational force acting on it. Hence, option (b) is the correct answer.
Question: A cyclist rides a bicycle with a wheel radius of 0.500 m across campus. A piece of plastic on the front rim makes a clicking sound every time it passes through the fork. If the cyclist counts 320 clicks between her apartment and the cafeteria, how far has she travelled? (a) 0.50 km (b) 0.80 km (c) 1.0 km (d) 1.5 km (e) 1.8 km
A car traveling on a flat (unbanked), circular track accelerates uniformly from rest with a tangential acceleration of . The car makes it one-quarter of the way around the circle before it skids off the track. From these data, determine the coefficient of static friction between the car and the track.
Question: Suppose a car’s standard tires are replaced with tires 1.30 times larger in diameter. (i) Will the car’s speedometer reading be (a) 1.69 times too high, (b) 1.30 times too high, (c) accurate, (d) 1.30 times too low, (e) 1.69 times too low, or (f) inaccurate by an unpredictable factor? (ii) Will the car’s fuel economy in miles per gallon or km/L appear to be (a) 1.69 times better, (b) 1.30 times better, (c) essentially the same, (d) 1.30 times worse, or (e) 1.69 times worse?
A disk 8.00 cm in radius rotates at a constant rate of 1200 rev / min about its central axis. Determine (a) its angular speed in radians per second, (b) the tangential speed at a point 3.00 cm from its center, (c) the radial acceleration of a point on the rim, and (d) the total distance a point on the rim moves in 2.00 s.
The hour hand and the minute hand of Big Ben, the Elizabeth Tower clock in London, are long and have masses of kg, respectively (see Fig. ).
(a) Determine the total torque due to the weight of these hands about the axis of rotation when the time reads . (You may model the hands as long, thin, uniform rods.)
(b) Determine all times when the total torque about the axis of rotation is zero. Determine the times to the nearest second, solving a transcendental equation numerically
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