221 – Lab 7 Rotational Motion and The Moment of Inertia E, = E, %3D K, +Ug0 +K„, = K, +Ugs +K,s 8,0 `r,0 8,f 1 m,V½,o +m„gY,0 +÷Io 1 m,v +m„gYh,s 2 + "h°h,0 ´h,f Note the position of the hanging mass is y,, and its velocity is v,. The moment of inertia is I for whatever is rotating. 1. Isolate the moment of inertia, algebraically from the above equation as all other variables have been measured.

A figure skater performs a twisting jump. She rotates around her longitudinal axis 2 times in 0.65 s. What was her angular displacement in radians? A 4 В D 720 E 2m

Consider the rotational kinematic motion profile indicated below. t: 0 → 5 s = 0 deg/s , R O(0) = 0 deg = 0 deg/s Y(0) = 0 deg = 6 deg/s , Q Ф(0) = 0 deg O deg %3D t: 5 → 15 s P = 0 deg/s Ó = 6 deg/s Ý(t) = 3/cos(0(t)) deg/s Compute roll angle O at t = 15 s.

A plane with a wingspan of d = 16 m loses control in flight and begins to spiral in a circle around the cockpit while in a vertical dive. It completes one rotation every t = 3.1 s.

h A solid sphere rolls without slipping down an incline. At the top it is at rest. What is the linear speed at the bottom? Parameters: ] mass = m = 4.3 kg; angle of the incline height of the ramp = h = 1.10 m; horizontal length of the ramp = L = 3.02 m. (in m/s) = 20 degrees; A: 3.356 OB: 3.926 OC: 4.594 OD: 5.375 OE: 6.288 OF: 7.357 OG: 8.608 OH: 1.007x10¹

Macmillan l A motorized wheel is spinning with a rotational velocity of wo = 1.81 rad/s. At t = 0s, the operator switches the wheel to a higher speed setting. The rotational velocity of the wheel at all subsequent times is given by w (t) = woarctan (c + b1²) where c = 1.5574 and b = 6.09 s-². At what time tamax is the rotational acceleration at a maximum? tamax = What is the maximum tangential acceleration a, of a point on the wheel a distance R = 1.29 m from its center? a₁ = What is the magnitude of the total acceleration of this point? a = ms m/s² m/s²

W; = 0 %3D Wf initial final A flywheel consists of a thin uniform disk of mass m and radius R, free to rotate about a frictionless central axle. A small weight, also of mass m, is attached to the wheel's rim. The is wheel is held at rest (left), the small weight level with the axle, then released. What is the angular velocity of the wheel when the weight reaches its lowest point? 4g V 3R 8g V 5R 3g V 2R V28R 2gR

Compute the combined moment of the two 80-lb forces about (a) point O and (b) point A. The moment is positive if counterclockwise, negative if clockwise. Assume a = 5.0 in., b=2.7 in., F-80 lb. y 1 F Answers: (a) Mo i (b) MA-i Ib-in. lb-in.

A force F of magnitude 56 N is applied to the gear. Determine the moment (positive if counterclockwise, negative if clockwise) of F about point O. Assumer-195 mm, 0 = 32° Answer: Mo= i N-m

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