Exam 9: Rotation

In a fast rotating atomic nucleus the rate of rotation is related to the energy of the emitted gamma-ray according to the relationship "E_gamma = 2hf," where h = Planck's constant,and f = rotational frequency.Find the period of rotation that corresponds to an energy of 0.75 MeV.

A bicycle wheel,a hollow sphere,and a solid sphere each have the same mass and radius.They each rotate about an axis through their centers.Which has the greatest moment of inertia and which has the least?

What constant torque,in the absence of friction,must be applied to a wheel to give it an angular velocity of 50 rad/s if it starts from rest and is accelerated for 10 s? The moment of inertia of the wheel about its axle is 9.0 kg · m².

A wheel rotates through 6.0 rad in 2.0 s as it is uniformly brought to rest.The initial angular velocity of the wheel before braking began was

The rotational inertia of an object about an axis depends on the

For a hoop (ring)of mass M and radius R that is rolling without slipping,which is greater,its translational or its rotational kinetic energy?

A solid sphere of radius r = 5 cm and mass m = 0.2 kg rolls in a groove as shown.The angle, $\theta$ ,between the points of contact with the groove is 120 ^$\circ$ .If the sphere has a linear velocity of 10 mm/s,what is the rotational kinetic energy?

A disc is free to rotate about an axis.A force applied at a distance d from the axis causes an angular acceleration $\alpha$ .What angular acceleration is produced if the same force is applied a distance 2d from the axis?

Two points,A and B,are on a disk that rotates about an axis.Point A is closer to the axis than point B.Which of the following is not true?

A wheel rotates with a constant nonzero angular acceleration.Which of the following quantities remains constant in magnitude?

The disc brakes of a high performance car are often made of carbon fiber instead of iron,thereby reducing the mass.If both types of discs are of the same size and shape,and each iron disc has a mass of 4 kg and each carbon disc has a mass of 1 kg,what is the reduction in rotational kinetic energy at 72 km/h if all the four iron discs in the car are replaced with carbon discs?

The moment of inertia of a certain wheel about its axle is mR².The translational speed of its axle after it starts from rest and rolls without slipping down an inclined plane 2.13 m high is

Starting from rest at the same time,a coin and a ring roll down an incline without slipping.Which reaches the bottom first?

In the figure,R₁ = R₂ and cm is the center of mass.The rotational inertia about an axis through point P₁ is I₁,the rotational inertia about an axis through point P₂ is I₂,and the rotational inertia about an axis through the cm is I_cm.The relationship among the moments is

The moment of inertia of a slim rod about a transverse axis through one end is mL²/3,where m is the mass of the rod and L is its length.The moment of inertia of a 0.24-kg meterstick about a transverse axis through its center is

Two objects,m₁ and m₂,both of mass m,are place on a horizontal platform which is rotating at a constant angular velocity.m₁ is located at a distance R from the axis of rotation and m₂ is located at a R.The centripetal acceleration of mass m₁ ____ to the centripetal acceleration of m₂.

The torque exerted on a perfectly spherical satellite by the gravitational pull of the sun is

Two blocks m₁ (= 0.4 kg)and m₂ (= 0.6 kg)are initially positioned at x = 0.6 and x = 1.1m.One cord is used to couple the blocks together and another to attach m₁ to a vertical pole at the origin.The blocks are made to rotate in a horizontal circle on a frictionless surface.If the period of rotation is 0.4s then calculate the ratio of the tension for the inner cord divided by the tension in the outer cord.

A spherical shell and a solid sphere (both of the same total mass)are rotating about a diameter at the same angular frequency and with the same rotational kinetic energy.What is the ratio of the spherical shell radius to the solid sphere (i.e.,R_{spherical shell}/R_{solid sphere})?

A solid cylinder,a hollow cylinder,and a square block of equal masses are released at the top of an inclined plane.The cylinders roll down and the block slides down,all with negligible frictional losses.Which of the following will happen?