1. A particle is moving left to right at a height of y = 2.0 m and v = 5.0 m/s.
ID: 2111048 • Letter: 1
Question
1. A particle is moving left to right at a height of y = 2.0 m and v = 5.0 m/s. Its mass is 1.0 kg. a) What is it's linear momentum? b) If it starts at x = 0, what is its angular momentum as a function of time? (Use x=0, y=0 as the origin.) c) Based off of your results from a and b, is there any external torque on the particle?2. A guy is spinning initially at a constant rate with his arms at his sides. He then puts his arms straight out. His arms are 80 cm each and he has a wing span of 2.0 m. Each arm has a mass of about 10 kg (assume his arms are uniform cylinders.) a) How much does his moment of inertia change when he sticks his arms out? b) How much does his angular momentum change when he sticks his arms out?
3. On a pendulum, what is the total torque on a pendulum as a function of its angular position from normal. The pendulum is a string of length â„“ with a mass at the end of it, mass m.
4. A pencil falls from being balanced on its tip. It has length â„“ and uniform mass m. a) Use conservation of energy to find the angular velocity of the pencil as it hits the ground. b) Use result from part a to find the velocity of the center of mass as it hits the ground. c) Compare this to the velocity of a ball dropped from a height h = â„“/2.
5. What is the work done by friction, when rolling without slipping?
6. A bar of length .15 m, width .05 m and negligible height is spinning about its center of mass at 2 radians per second. A disk is then dropped onto the bar's center of mass. The disk has a radius of .05 m. If the two objects have the same mass, what is their final angular velocity?
7. Compare the time for different masses of the same radius and mass to roll down an incline if height h and angle theta. Find the times for a loop, a disk, a solid sphere and a shell sphere. Place them in order of fastest to slowest.
8. Using 4 uniform bricks of length â„“, what is the furthest you can get the top brick over the edge of a table without the stack toppling over? Measure from the edge of table horizontally to far edge of brick. 1. A particle is moving left to right at a height of y = 2.0 m and v = 5.0 m/s. Its mass is 1.0 kg. a) What is it's linear momentum? b) If it starts at x = 0, what is its angular momentum as a function of time? (Use x=0, y=0 as the origin.) c) Based off of your results from a and b, is there any external torque on the particle?
2. A guy is spinning initially at a constant rate with his arms at his sides. He then puts his arms straight out. His arms are 80 cm each and he has a wing span of 2.0 m. Each arm has a mass of about 10 kg (assume his arms are uniform cylinders.) a) How much does his moment of inertia change when he sticks his arms out? b) How much does his angular momentum change when he sticks his arms out?
3. On a pendulum, what is the total torque on a pendulum as a function of its angular position from normal. The pendulum is a string of length â„“ with a mass at the end of it, mass m.
4. A pencil falls from being balanced on its tip. It has length â„“ and uniform mass m. a) Use conservation of energy to find the angular velocity of the pencil as it hits the ground. b) Use result from part a to find the velocity of the center of mass as it hits the ground. c) Compare this to the velocity of a ball dropped from a height h = â„“/2.
5. What is the work done by friction, when rolling without slipping?
6. A bar of length .15 m, width .05 m and negligible height is spinning about its center of mass at 2 radians per second. A disk is then dropped onto the bar's center of mass. The disk has a radius of .05 m. If the two objects have the same mass, what is their final angular velocity?
7. Compare the time for different masses of the same radius and mass to roll down an incline if height h and angle theta. Find the times for a loop, a disk, a solid sphere and a shell sphere. Place them in order of fastest to slowest.
8. Using 4 uniform bricks of length â„“, what is the furthest you can get the top brick over the edge of a table without the stack toppling over? Measure from the edge of table horizontally to far edge of brick.
Explanation / Answer
FOLLOW THIS Momentum = mass * velocity for this problem the momentum of a mass M will be a function of velocity V. velocity will depend on how long the mass M falls which depends of height H. distance = H acceleration =A (in this case due to gravity) time = T ^2 means squared velocity = V momentum = P mass = M H = 1/2 AT^2 T = sqrt 2H/A V = AT P = MV
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