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Consider a rigid body that is rotating. Which of the following is an accurate statement?
Which of the following do not affect the maximum speed that a car can drive in a circle? Choose all correct answers.
A spherical balloon of mass \( 226 \) \( \text{kg} \) is filled with helium gas until its volume is \( 325 \) \( \text{m}^3 \). Assume the density of air is \( 1.29 \) \( \text{kg/m}^3 \) and the density of helium is \( 0.179 \) \( \text{kg/m}^3 \).
A \(25.0 \, \text{kg}\) box is released on a \(23.5^\circ\) incline and accelerates down the incline at \(0.35 \, \text{m/s}^2\). Find the friction force impeding its motion. What is the coefficient of kinetic friction?
A student is watching their hockey puck slide up and down an incline. They give the puck a quick push along a frictionless table, and it slides up a \( 30^\circ \) rough incline (\( \mu_k = 0.4 \)) of distance \( d \), with an initial speed of \( 5 \) \( \text{m/s} \), and then it slides back down.
A \( 1.5 \; \text{kg} \) mass attached to a spring with a force constant of \( 20.0 \; \text{N/m} \) oscillates on a horizontal, frictionless track. At \( t = 0 \), the mass is released from rest at \( x = 10.0 \; \text{cm} \). (That is, the spring is stretched by \( 10.00 \; \text{cm} \).)
A \(4.0 \, \text{kg}\) block is moving at \(5.0 \, \text{m/s}\) along a horizontal frictionless surface toward an ideal spring that is attached to a wall. After the block collides with the spring, the spring is compressed a maximum distance of \(0.68 \, \text{m}\). What is the speed of the block when the spring is compressed to only one-half of the maximum distance?
A theme park ride consists of a large vertical wheel of radius \( R \) that rotates counterclockwise on a horizontal axle through its center. The cars on the wheel move at a constant speed \( v \). Points \( A \) and \( D \) represent the position of a car at the highest and lowest point of the ride, respectively. While passing point \( A \), a student releases a small rock of mass \( m \), which falls to the ground without hitting anything. Which of the following best represents the kinetic energy of the rock when it is at the same height as point \( D \)?
A sphere starts from rest and rolls down an incline of height \( H = 1.0 \) \( \text{m} \) at an angle of \( 25^\circ \) with the horizontal, as shown above. The radius of the sphere \( R = 15 \) \( \text{cm} \), and its mass \( m = 1.0 \) \( \text{kg} \). The moment of inertia for a sphere is \( \frac{2}{5}mR^2 \). What is the speed of the sphere when it reaches the bottom of the plane?
A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of \( 70 \, \text{cm} \) as she throws. She releases the \( 600 \, \text{g} \) javelin \( 2.0 \, \text{m} \) above the ground traveling at an angle of \( 30^\circ \) above the horizontal. In this throw, the javelin hits the ground \( 54 \, \text{m} \) away. Find the following:
A moderate force will break an egg. However, an egg dropped on the road usually breaks, while one dropped on the grass usually does not break because for the egg dropped on the grass:
Suppose we wish to make a neutrally buoyant hollow sphere out of titanium (\(\rho = 4500 \text{kg/m}^3\)). If the sphere has an outer radius of \( 1.5 \) \( \text{m} \), what must be its inner radius?
A point on the edge of a disk rotates around the center of the disk with an initial angular velocity of 3 rad/s clockwise. The graph shows the point’s angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible.
You stand at the edge of a vertical cliff and throws a stone vertically upwards. The stone leaves your hand with a speed v = 8.0 m/s. The time between the stone leaving your hand and hitting the sea is 3.0 s. Assume air resistance is negligible. Calculate:
A projectile is launched at angle \( \theta \) to the horizontal, with velocity \( v \), maximum vertical displacement \( s \), and angle \( \theta \) between \( 0^{\circ} \) and \( 45^{\circ} \). What will the maximum vertical displacement be if the projectile is now launched at an angle of \( 2 \theta \) from the horizontal with velocity \( v \)?
A \(25 \, \text{g}\) steel ball is attached to the top of a \(24 \, \text{cm}\)-diameter vertical wheel of negligible mass. Starting from rest, the wheel accelerates at \(470 \, \text{rad/s}^2\). The ball is released after \(\frac{3}{4}\) of a revolution. How high does it go above the center of the wheel?
Can an object have a non-zero distance and zero average speed?
Consider a solid uniform sphere of radius \(R\) and mass \(M\) rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?
A 45 kg crate accelerates at 1.65 m/s2 when pulled by a rope with a force of 200 N. Find the angle the rope is pulled at. Friction is negligible.
Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy?
A solid sphere of mass \( 1.5 \, \text{kg} \) and radius \( 15 \, \text{cm} \) rolls without slipping down a \( 35^\circ\) incline that is \( 7 \, \text{m} \) long. Assume it started from rest. The moment of inertia of a sphere is \( I= \frac{2}{5}MR^2 \).
Find the following three values using just rotational kinematics.
The exoplanet HD 69830b has a mass 10 times that of the Earth and a radius 5 times that of the Earth. The value of g on HD 69830b is most nearly
Four forces are exerted on a disk of radius \( R \) that is free to spin about its center, as shown above. The magnitudes are proportional to the length of the force vectors, where \( F_1 = F_4 \), \( F_2 = F_3 \), and \( F_1 = 2F_2 \). Which two forces combine to exert zero net torque on the disk?
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