Competitive ice skaters commonly perform single, double, and triple axel jumps in which they rotate 1 1 2 , 2 1 2 , and 3 1 2 revolutions, respectively, about a vertical axis while airborne. For all these jumps, a typical skater remains airborne for about 0.70 s. Suppose a skater leaves the ground in an “open” position (e.g., arms outstretched) with moment of inertia I 0 and rotational frequency f 0 = 1.2 rev/s, maintaining this position for 0.10 s. The skater then assumes a “closed” position (arms brought closer) with moment of inertia I , acquiring a rotational frequency f , which is maintained for 0.50 s. Finally, the skater immediately returns to the “open” position for 0.10 s until landing (see Fig. 11–49). ( a ) Why is angular momentum conserved during the skaters jump? Neglect air resistance. ( b ) Determine the minimum rotational frequency f during the flight’s middle section for the skater to successfully complete a single and a triple axel. ( c ) Show that, according to this model, a skater must be able to reduce his or her moment of inertia in midflight by a factor of about 2 and 5 in order to complete a single and triple axel, respectively.
Competitive ice skaters commonly perform single, double, and triple axel jumps in which they rotate 1 1 2 , 2 1 2 , and 3 1 2 revolutions, respectively, about a vertical axis while airborne. For all these jumps, a typical skater remains airborne for about 0.70 s. Suppose a skater leaves the ground in an “open” position (e.g., arms outstretched) with moment of inertia I 0 and rotational frequency f 0 = 1.2 rev/s, maintaining this position for 0.10 s. The skater then assumes a “closed” position (arms brought closer) with moment of inertia I , acquiring a rotational frequency f , which is maintained for 0.50 s. Finally, the skater immediately returns to the “open” position for 0.10 s until landing (see Fig. 11–49). ( a ) Why is angular momentum conserved during the skaters jump? Neglect air resistance. ( b ) Determine the minimum rotational frequency f during the flight’s middle section for the skater to successfully complete a single and a triple axel. ( c ) Show that, according to this model, a skater must be able to reduce his or her moment of inertia in midflight by a factor of about 2 and 5 in order to complete a single and triple axel, respectively.
Competitive ice skaters commonly perform single, double, and triple axel jumps in which they rotate
1
1
2
,
2
1
2
, and
3
1
2
revolutions, respectively, about a vertical axis while airborne. For all these jumps, a typical skater remains airborne for about 0.70 s. Suppose a skater leaves the ground in an “open” position (e.g., arms outstretched) with moment of inertia I0 and rotational frequency f0 = 1.2 rev/s, maintaining this position for 0.10 s. The skater then assumes a “closed” position (arms brought closer) with moment of inertia I, acquiring a rotational frequency f, which is maintained for 0.50 s. Finally, the skater immediately returns to the “open” position for 0.10 s until landing (see Fig. 11–49). (a) Why is angular momentum conserved during the skaters jump? Neglect air resistance. (b) Determine the minimum rotational frequency f during the flight’s middle section for the skater to successfully complete a single and a triple axel. (c) Show that, according to this model, a skater must be able to reduce his or her moment of inertia in midflight by a factor of about 2 and 5 in order to complete a single and triple axel, respectively.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
A ceiling fan with 84-cmcm-diameter blades is turning at 64 rpmrpm . Suppose the fan coasts to a stop 29 ss after being turned off.
a) What is the speed of the tip of a blade 10 ss after the fan is turned off? Express your answer with the appropriate units.
b) Through how many revolutions does the fan turn while stopping?
A four-bit Gray cyclic code A, where A = A3A2A¡Ao with Ao as the least significant digit, is used
to represent ten angular positions of a wheel, the cyclic code being as follows:
Input Code A
A3 A2 Aj Ao
Position
1
1
1
1
3
1
1
1
4
1
1
5
1
1
6
1
1
1
1
1
8
1
1
9
1
The remaining six possible combinations of A3A2A1A0 never occur. A recoding circuit accepts
this cyclic code and gives an output code that is equal to the decimal position number but in
natural binary coding.
(a)
Identifying the output code as B = B3B2B¡Bo in your answer, where Bo is the least
significant digit, compile a truth table that completely specifies the required recoding
circuit.
(b)
Derive the sum-of-minterms the Boolean expressions for the required outputs.
A record rotates through 5.6 radians as it slows down uniformly from 78.0rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record?
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