1. Consider a race car that moves with a speed of 193 mi/h. If it travels on a c
ID: 2296296 • Letter: 1
Question
1. Consider a race car that moves with a speed of 193 mi/h. If it travels on a circular race track of circumference 2.6 mi, what is the car's angular speed? (in rad/s PLEASE)
2. A person carries a long pole of mass 12 kg and length 4.2 m as shown in the figure below. If the length of the pole is increased by a factor of two and its mass is increased by a factor of five, by what factor does the torque change?
3. Consider a merry-go-round that has the form of a disc with radius 5.1 m and mass 150 kg. If two children, each of mass 20 kg, sit on the outer edge of the merry-go-round, what is the total moment of inertia?
_______ kg m^2
Explanation / Answer
1. Circumference = 2*pi*r = 2.6 mi
Hence, r = 0.414 mi
angular speed = v/r = (193*2*pi/3600)/0.414 = 0.814 rad/s
2. Torque = mg*(l/2)*cos 60
Torque changes by 2*5 = 10 times.
3. Moment of inertia = (1/2)*m*r^2 + 2*M*r^2 = 0.5*150*5.1^2 + 2*20*5.1^2 = 2991.15 kg-m^2
4. Let Forces at P on flagpole are Rx and Ry in x and y direction respectively.
Taking torque about P: (Tsin29)*10 = mg*5
Hence, T = (21*9.8*5)/(10*sin29) = 212.25 N
Force balance in x direction, Rx=Tcos29 = 185.636 N
Force balance in y direction, Ry = mg-Tsin29 = 102.9 N
Net force = sqrt(185.636^2+102.9^2) = 212.248 N acting at angle of arctan(102.9/185.636) = 29 degree counterclockwise from the +x-axis
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