An oversized yo-yo is made from two identical solid disks each ofmass M = 1.90 kg and radius R = 11.6 cm. The two disks are joinedby a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg asin the figure below. Take the center of the cylinder as the axis ofthe system.
(a) What is the moment of inertia of the system? Give a symbolicanswer. (Use any variable or symbol stated above asnecessary.)
moment of inertia =
(b) What torque does gravity exert on the system with respect tothe given axis?
2.
Take downward as the negative coordinate direction.
(c) As depicted in the figure above, is the torque exerted by thetension positive or negative? (View the yo-yo from the left and letthe counterclockwise direction be positive.)
3. positive or negative
(d) Is the angular acceleration positive or negative?
4. positive or negative
(e) What about the translational acceleration?
5. positive or negative
(f) Write an equation for the angular acceleration a (alpha) interms of the translational acceleration a and radius r. (Watch thesign!)
a =
(g) Write Newton's second law for the system in terms of m, M, a,T, and g. (Do this on paper. Your instructor may ask you to turn inthis work.)
(h) Write Newton's second law for rotation in terms of I, a, T, andr. (Do this on paper. Your instructor may ask you to turn in thiswork.)
(i) Eliminate a from the rotational second law with the expressionfound in part (f) and find a symbolic expression for theacceleration a in terms of m, M, g, r and R.
a =
(j) What is the numeric value for the system's acceleration?
8. m/s2
(k) What is the tension in the string?
9. N
(l) How long does it take the system to drop 1.20 m fromrest?
10 s
An oversized yo-yo is made from two identical solid disks each ofmass M = 1.90 kg and radius R = 11.6 cm. The two disks are joinedby a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg asin the figure below. Take the center of the cylinder as the axis ofthe system.
(a) What is the moment of inertia of the system? Give a symbolicanswer. (Use any variable or symbol stated above asnecessary.)
moment of inertia =
(b) What torque does gravity exert on the system with respect tothe given axis?
2.
Take downward as the negative coordinate direction.
(c) As depicted in the figure above, is the torque exerted by thetension positive or negative? (View the yo-yo from the left and letthe counterclockwise direction be positive.)
3. positive or negative
(d) Is the angular acceleration positive or negative?
4. positive or negative
(e) What about the translational acceleration?
5. positive or negative
(f) Write an equation for the angular acceleration a (alpha) interms of the translational acceleration a and radius r. (Watch thesign!)
a =
(g) Write Newton's second law for the system in terms of m, M, a,T, and g. (Do this on paper. Your instructor may ask you to turn inthis work.)
(h) Write Newton's second law for rotation in terms of I, a, T, andr. (Do this on paper. Your instructor may ask you to turn in thiswork.)
(i) Eliminate a from the rotational second law with the expressionfound in part (f) and find a symbolic expression for theacceleration a in terms of m, M, g, r and R.
a =
(j) What is the numeric value for the system's acceleration?
8. m/s2
(k) What is the tension in the string?
9. N
(l) How long does it take the system to drop 1.20 m fromrest?
10 s
