Physics Rotational Mechanics Level: University
Center of MassA uniform thin machine part is a flat circular plate of radius 2R that has a circular hole of radius R cut out of it. The centre of the hole is a distance 0.8 R from the centre of the plate. What is the position of the centre of mass of the plate (Think of a solid plate as being the sun of the given plate plus a small one of radius R)
Physics Rotational Mechanics Level: University
TorqueAssume a cyclist of weight mg can exert a force on the pedals equal to 0.9 mg on the avereage. Assume the mass of the bike is 12 kg and that of the rider is 60 kg . If the pedals rotate in a circle of radius 18 cm/the wheels have a radius of 34 cm, and the front and back sprockets on which the chain runs have 42 and 19 teeth respectively determine the maximum steepness of hill the cyclist can climb at constant speed. Ignore friction. Assum the cyclistss avg force is always a) downard b ) tangential to pedal motion.
Physics Rotational Mechanics Level: University
Conservation of momentumA rigid bar is suspended in the air on a frictionless pivot )at the top of the bar). The bar is uniform and has a mass M and length L.A small bullet is shot into the bottom end of the bar. The bullet has mass m and hits the rod moving horizontally with speed v. ( recall that the moment of inertia of a uniform rod about an axis perpendicular to the rod and through the center of mass is ML^2/12). Express your answer in terms of any/all of m M L g v.
1. Derive an expression for the angular velocity of the rod + bullet ( about the pivot) immediately after the collision.
2. Derive an expression for the maximum angle of deflection of the rod after the collision.
3. Derive an expression for the horizontal linear momentum impulse delivered to the rod by the pivot during the collision.
Physics Rotational Mechanics Level: University
TorqueA yo-yosits initially at rest on a table top. The coefficient of static friction between the yo-yo and surface of the table is 6/10. The yo-yo consists of two disks with a rather thick central spindle around which is wrapped some string of negligible mass. the moment of inertia of the yo-yo is 2/5 m R^2 where R is the outer radius of the yo-yo and M is its mass. The radius of the spindle is R/4. Neglect the thickness of the thin massles string.
A persion pulls straight up on the string with an applied force F.
What is the largest HORIZONTAL acceleration that can be given to the yo-yo-by method. Express your answer as a multiple of g.
Physics Rotational Mechanics Level: University
Rotational MotionA car accelerates uniformly from rest to a maximum speed of 27 m/sec in a time of 30 seconds. Each wheel has a radius of .36 m and a mass of 20 kg. Calculate the angular momentum of each wheel the angular acceleration of the wheels ( alpha) and the angular velocity (omega).
Physics Rotational Mechanics Level: University
Equation of Rotational MotionThe certain amusement park merry-go-round, moving at its constant operational speed, takes 60 s to complete one complete rotation. Two children are riding hourses one at 3.0 m form the center and the second at 6.0 m from the center. Find the angular speed for each child. Find the linear or tangential speed for each child. If it takes two minutes for the rode to reach its constant operational speed What is the angular acceleration?
Physics Rotational Mechanics Level: University
Rotational MotionA 60.0-kg skater begins a spin with an angular speed of 6.0 rad/s. By changing the position of her arms the skater decreases her moment of inertia by 50 persent.What is the skaters final angular speed?
Physics Rotational Mechanics Level: University
Rotational MotionA string is wrapped around a pulley of radius 0.10 m and moment of inertia 0.15 kg.m2. The string is pulled with a force of 12N. What is the magnitude of the resulting angular acceleration of the pulley?
Physics Rotational Mechanics Level: University
Rotational MotionA 50 N.m torque acts on a wheel of moment of inertia 150 kg.m2. If the wheel starts from rest how long will it take the wheel to make one revolution?
Physics Rotational Mechanics Level: University
Rotational MotionA meter stick is pivoted at the 0.50-m line. A 3.0 - kg object is hung from the 0.10-m line. Where should a 5.0-kg object be hung to achieve equilibrium?
Physics Rotational Mechanics Level: High School
A thin hoop with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 3.5 rad/s .What is the kinetic energy ?a) 0.18 J
b) 0.092 J
c) 1.05 J
Physics Rotational Mechanics Level: High School
A soccer ball whose radius is 11 cm rolls a distance of 10 m in 3.50 s , What is the angular speed of the ball ?a) 13 m/s
b) 26 m/s
c) 39 m/s
d) 52 m/s
Physics Rotational Mechanics Level: High School
Uniform circular motion
A child is riding a merry-go-round which completes one revolution every 8.36 s . The child is standing 4.65 m from the center of the merry-go-round . What is the tangential speed of a child ?
a) 5.64 m/s
b) 3.49 m/s
c) 0.556 m/s
d) 1.80 m/s
Physics Rotational Mechanics Level: High School
Rotational Kinematics
A wheel rotates through an angle of 13.8 rad as it slows down from 22.0 rad/s to 13.5 rad/s . What is the magnitude of the average angular acceleration of the wheel ?
a) 0.616 rad/s squared
b) 111 rad/s squared
c) 22.5 rad/s squared
d) 10.9 rad/s squared
Physics Rotational Mechanics Level: High School
Rotational Kinematics
A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s to power of (exponent) .Through wha angle has the wheel turned when its angular speed reaches 72.0 rad/s ?
a) 83.2 rad
b) 697 rad
c) 66.8 rad
d) 948 rad
