A disk shaped yoyo (m=220 grams) has a 70 cm long string. The radius of the central winding peg is 2.5 mm, the outer radius of the yoyo is 5.6 cm.
A) How much Torque is applied to this yoyo by the string?
B) How long until the yoyo hits the bottom of the throw?
C) What is the total kinetic energy of the yoyo just before it hits this point?
D) Several Yoyo’s instead of using a disk shape, use half hemispheres. What SPECIFIC advantage would this give the yoyo?
A) To calculate the torque applied to the yoyo by the string, we need to use the formula for torque: torque = force x distance. The force applied by the string can be calculated using the equation force = mass x acceleration. In this case, the acceleration is the centripetal acceleration of the yoyo, which is given by the equation acceleration = (angular velocity)^2 x radius.
First, convert the string length from cm to meters: 70 cm = 0.7 m.
Next, convert the outer radius of the yoyo from cm to meters: 5.6 cm = 0.056 m.
Convert the string radius from mm to meters: 2.5 mm = 0.0025 m.
The angular velocity (ω) of the yoyo can be calculated using the equation ω = v / r, where v is the linear velocity of the yoyo and r is the radius of the outer edge of the yoyo.
The linear velocity (v) can be calculated using the equation v = 2πr / time, where time is the time taken for the yoyo to travel the string length.
B) To calculate the time taken for the yoyo to hit the bottom of the throw, we'll use the equation for time: time = distance / speed.
The distance is the length of the string, which is 70 cm. The speed is the linear velocity of the yoyo, which we calculated in part A.
C) The total kinetic energy of the yoyo just before it hits the bottom of the throw can be calculated using the equation K.E. = 0.5 x mass x (linear velocity)^2.
D) The specific advantage of using half hemispheres instead of a disk shape for yoyos is that the distribution of mass is more centralized towards the outer edge. This results in a higher moment of inertia, which makes the yoyo more stable and increases its spin time. The additional mass concentrated at the outer edge helps to maintain angular momentum and resist slowing down.