1. What is the angular velocity of the wheel (in rad/s) at t = 5.0 s? 2. What is

Question

1. What is the angular velocity of the wheel (in rad/s) at t = 5.0 s?
2. What is the angular acceleration of the wheel (in rad/s2) before t = 5.0 s?
3. What is the acceleration of the hanging mass (in m/s2) during the time when the wheel's speed is increasing?
4. What is the tension in the string (in N) while the wheel's speed is increasing? (Tip: Draw the free-body diagram of the mass. You should have two forces.)
5. Determine the torque exerted on the wheel by the string while the wheel's speed is increasing.
6. Finally, determine the moment of inertia of the wheel. (You may assume here that the only signifcant torque acting on the wheel is that due to the string, i.e., torque due to frictional drag is negligible.)

Consider a bicycle wheel with a radius of 30 cm and 16 spokes that is mounted with its axle fixed in a horizontal position. The number of spokes that pass close to an electronic eye are counted and registered on a computer. This meausre of the rate at which the wheel turns is used to observe the wheel's motion when a 50 g mass is hung from a string wrapped around the periphery of the tire. The wheel is held stationary with the weight hanging as shown and then released 1. What is the angular velocity of the wheel (in rad/s) at t = 5.0 s? 2. What is the angular acceleration of the wheel (in rad/s^2) before t = 5.0 s? 3. What is the acceleration of the hanging mass (in m/s^2) during the time when the wheel's speed is increasing? 4. What is the tension in the string (in N) while the wheel's speed is increasing? (Tip: Draw the free - body diagram of the mass. You should have two forces.) 5. Determine the torque exerted on the wheel by the string while the wheel's speed is increasing. 6. Finally, determine the moment of inertia of the wheel. (You may assume here that the only signifcant torque acting on the wheel is that due to the string, i.e., torque due to frictional drag is negligible.) The wheel starts to spin, and spins faster and faster until the string slips off 5 second after release. The readings of the display device are summarized in the graph below.

Explanation / Answer

1. What is the angular velocity of the wheel (in rad/s) at t = 5.0 s? w=10(spokes/second)=3.9(rad/s) 2. What is the angular acceleration of the wheel (in rad/s2) before t = 5.0 s? phi=3.9/5=0.78(rad/s2) 3. What is the acceleration of the hanging mass (in m/s2) during the time when the wheel's speed is increasing? 0.78*0.3=0.234(m/s) 4. What is the tension in the string (in N) while the wheel's speed is increasing? (Tip: Draw the free-body diagram of the mass. You should have two forces.) Newton equation of motion:. mg-T=a*m. so T=m*(g-a)=0.48(N) 5. Determine the torque exerted on the wheel by the string while the wheel's speed is increasing. 0.48*0.3=0.143(Nm) 6. Finally, determine the moment of inertia of the wheel. (You may assume here that the only signifcant torque acting on the wheel is that due to the string, i.e., torque due to frictional drag is negligible.) we have 0.143/I=0.78 so I=0.183(kgm2)

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.