Practice Problems 12
1. What is the magnitude of the angular momentum of a 221.0g particle travelling 2.46m/s at position (x,y)=(1.49m, 2.06m)?
Answer: 1.12e+00 kg*m^2/s
2.Given M=5.50i+1.93j-1.26k and N=2.22i-1.31j-3.40k, calculate the vector product M×N. Answer in the order xyz or ijk.
Answer: -8.21E+00 1.59E+01 -1.15E+01
3. A 1.50kg particle moves in the xy plane with a velocity of v=(4.21i-3.76j)m/s. Determine the magnitude of the particle's angular momentum about the origin when its position vector is r=(1.69i+2.55j)m.
Answer: 2.56E+01 kg*m^2/s
4. The position vector of a particle of mass 2.46kg is given as a function of time by r=(6.01i+4.30t j)m. Determine the magnitude of the angular momentum of the particle about the origin.
Answer: 6.36E+01 kg*m^2/s
5. A uniform solid sphere with a radius of 0.445m and a mass of 16.2kg turns counterclockwise about a vertical axis through its center. Calculate the magnitude of its angular momentum when its angular speed is 2.81rad/s.
Answer: 3.61E+00 kg*m^2/s
6. A solid, horizontal cylinder of mass 10.6kg and radius 1.12m rotates with an angular speed of 6.93rad/s about a fixed vertical axis through its center. A 0.213kg piece of putty is dropped vertically onto the cylinder at a point 0.876m from the center of rotation, and sticks to the cylinder. Determine the final angular speed of the system.
Answer: 6.76e+00 rad/s
7. A space station shaped like a giant wheel has a radius of 123m and, when empty, a moment of inertia of 5.27×108kg·m2. A crew of 178 are living on the rim, and the station's rotation causes the crew to experience an acceleration of 1.00g.
When 139 people move to the center of the station for a meeting, the angular speed changes. What acceleration is experienced by the people remaining at the rim? Assume that the average mass of each inhabitant is 69.5kg.
Answer: 1.55E+01 m/s^2
7. A solid, horizontal cylinder of mass 10.6kg and radius 1.12m rotates with an angular speed of 6.93rad/s about a fixed vertical axis through its center. A 0.213kg piece of putty is dropped vertically onto the cylinder at a point 0.876m from the center of rotation, and sticks to the cylinder. Determine the final angular speed of the system.
Answer: 6.76e+00 rad/s
8. The puck in the figure below has a mass of 0.105kg.
Its original distance from the center of rotation is 41.3cm, and the puck is moving with a speed of 71.5cm/s. The string is pulled downward 13.2cm through the hole in the frictionless table. Determine the work done on the puck.
Answer: 3.11e-02 J
9. A 2.76kg, 29.5cm diameter turntable rotates at 102.0rpm on frictionless bearings. Two 541.0g blocks fall from above, hit the turntable simultaneously at opposite ends of a diagonal, and stick. What is the turntable's angular velocity, in rad/s, just after this event?
Answer: 5.99e+00 rad/s
10. An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0.00s. It then oscillates with a period of 11.8s and a maximum speed of 55.0cm/s. What is the amplitude of the oscillation?
Answer: 1.03e+00 m
11. What is the glider's position at t=0.684s?
Answer: 9.65e-01 m
12. What is the frequency of the oscillation shown if t1=16.0s and A=30.0cm?
Answer: 1.25e-01 Hz
13. What is the phase constant? Use a cosine function to describe the simple harmonic motion.
Answer: -2.09e+00 rad
14. What is the phase at t1?
Answer: 1.05e+01 rad
15. An object in simple harmonic motion has amplitude 6.90cm and frequency 0.310Hz, and at t=0.00s it is at its largest negative distance from the equilibrium position. What is the angular frequency?
Answer: 1.95e+00 rad/s
16. What is the phase constant assuming a cosine function to describe the motion?
Answer: 3.14e+00 rad