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SoulInNeed
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1.1. What are the SI units of angular velocity? Why?
2. Imagine a baton twirler is spinning a baton about its center. Which would increase its rotational kinetic energy more: doubling the angular velocity of the baton while keeping the mass and length the same, or doubling the length of the baton while keeping the mass and angular velocity the same (or would they have the same effect)? Why?
3. I find two rocks (call them "Rock A" and "Rock B") and tie them to the end of strings, and spin each rock around in a circle from the other end of the string. Rock A and B have the same angular velocity, but Rock A has a faster linear velocity than Rock B as they swing around. Which of the following must be true?
Rock A has a larger mass than Rock B.
Rock B has a larger mass than Rock A.
Rock A has a longer string than Rock B.
Rock B has a longer string than Rock A.
4. Explain your answer to the multiple choice question above.
3.1. The unit for angular velocity is rad/s, because unlike linear velocity, which measures change in coordinate displacement over time, angular velocity measures change in angular displacement (measured in radians) over time.
2. They have the same effect, because mathematically speaking, doubling the length of the baton will increase the moment of inertia for the baton ((1/12)*M*L^2) in the overall kinetic equation to the same level of the angular velocity if it was doubled. Essentially, whether you double the angular velocity or the length of the baton, they mathematically have the same effect on the kinetic equation.
3. Rock A has a longer string than Rock B.
4. The relation between linear velocity and angular velocity is v=r*w, if they both have the same angular velocity, then the difference in this case must be the radius of the string. If Rack A has a faster linear velocity, then it must have a longer string.
Thanks for any help!
2. Imagine a baton twirler is spinning a baton about its center. Which would increase its rotational kinetic energy more: doubling the angular velocity of the baton while keeping the mass and length the same, or doubling the length of the baton while keeping the mass and angular velocity the same (or would they have the same effect)? Why?
3. I find two rocks (call them "Rock A" and "Rock B") and tie them to the end of strings, and spin each rock around in a circle from the other end of the string. Rock A and B have the same angular velocity, but Rock A has a faster linear velocity than Rock B as they swing around. Which of the following must be true?
Rock A has a larger mass than Rock B.
Rock B has a larger mass than Rock A.
Rock A has a longer string than Rock B.
Rock B has a longer string than Rock A.
4. Explain your answer to the multiple choice question above.
Homework Equations
v=r*w, moment of inertia for slender rod, axis through center I=(1/12)*M*L^2, Kinetic Energy=(1/2)*I*w^23.1. The unit for angular velocity is rad/s, because unlike linear velocity, which measures change in coordinate displacement over time, angular velocity measures change in angular displacement (measured in radians) over time.
2. They have the same effect, because mathematically speaking, doubling the length of the baton will increase the moment of inertia for the baton ((1/12)*M*L^2) in the overall kinetic equation to the same level of the angular velocity if it was doubled. Essentially, whether you double the angular velocity or the length of the baton, they mathematically have the same effect on the kinetic equation.
3. Rock A has a longer string than Rock B.
4. The relation between linear velocity and angular velocity is v=r*w, if they both have the same angular velocity, then the difference in this case must be the radius of the string. If Rack A has a faster linear velocity, then it must have a longer string.
Thanks for any help!
