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.
Double collar C is articulated so that one of the rings slides on the stationary rod and the other on the rotating rod AB. Determine the required constant angular velocity ?̇ for rod AB, since the mechanism is designed to have a maximum speed of 6m / s that can be given to the ring. The path followed on the fixed bar is r = 0.4 sin ? + 0.2 ?.
An elevator cable winds on a drum of radius 76.2 cm that is connected to a motor.
a. If the elevator moves down at 0.330 m/s, what is the angular speed of the drum? answer in rad/s
b. If the elevator moves down 6.50 m, how many revolutions has the drum made? answer in rev
c. If the elevator moves down at 0.330 m/s, what is the drum’s frequency of rotation? answer in Hz
Calculate the angular frequency ω (in rad/s) with these numbers:
k = 5100 N/m = 5100 kg/s2
m1 = 30 kg
m2 = 25 kg
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.