1. You are designing a wheel that must have a fixed mass and diameter, but that

Question

1. You are designing a wheel that must have a fixed mass and diameter, but that can have its mass distributed in various uniform ways. If the torque you exert on it is also fixed, which of the wheels shown will have the largest angular acceleration about an axis perpendicular to it at its center? C. D. A) A, B) B,C)C, D) D, E) Both B and C A ball thrown horizontally from the top of a building hits the ground in 3.0s. If it had been thrown with three times the speed in the same direction, it would have hit the ground in 2. A) 1.0s, B) 3.0s, C) 9.0s, D) 6.0s, E) 1.5s Three objects are moving along a straight line as shown in the figure below. Taking the positive direction to be to the right, what is the total momentum of this system? 3. 5.00 m/s 4.00 m/s 2.00 m/s 8.00 kg 15.0 kg 3.00 kg A) +106 kg m/s, B)-106 kg m/s, C)+14 kg m/s, D)-14 kg m/s, E) 0 kg m/s 4. A force of 16.88 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular acceleration of 1.20 rad/s2. Calculate the rotational inertia of the wheel. A) 3.59 kg m2, B) 4.78 kg m2, C)5.98 kg m2, D)7.17 kg m2, E) 14.1 kg m2 You install two rope swings from a tree in your yard. The rope for swing A is half as long as the rope for swing B. Assuming they behave like ideal pendulums, how do their periods compare? 5.

Explanation / Answer

(1) We know

Torque=Moment of inertia*angular accleration

so whose moment of inertia is less,will have more angular acceleration

Since mass is same ,where mass is uniformly distributed will have less moment of inertia so

(A) will have largest angular acceleration

(2)

since height is same

and velocity is increased horizontally so it will not affect vertical motion so time will be same

so time is 3 sec

(3)Total momentum=40-60+6=-14 kgm/s

(4) I=Torque/angular acceleration=16.88*0.34/1.2=4.78 kgm^2

(5) Since Time period is 2*pi*sqrt(l/g)

so more is length more is period

so TA=TB/sqrt(2)=sqrt(2)*Ta=Tb

option (e) is correct

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