A 6-kg box on a frictionless horizontal surface is attached to a horizontal spring with a force constant of $800 \mathrm{~N} / \mathrm{m}$. If the spring is stretched $4 \mathrm{~cm}$ from its equilibrium length, what is the acceleration of the box?

A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes over a frictionless pulley. The pulley has the shape of a uniform solid disk of mass 2.00 kg and diameter 0.500 m. After the system is released, find the tension in the wire on both sides of the pulley,

A 2.50-kg grinding wheel is in the form of a solid cylinder of radius 0.100 m.

A) What constant torque will bring it from rest to an angular speed of 1200 rev/min in 2.5 s?

B) Through what angle has it turned during that time?

C) Use equation $W=\tau\cdot(\theta_2-\theta_1)=\tau \cdot \Delta \theta$ to calculate the work done by the torque.

D) What is the grinding wheel’s kinetic energy when it is rotating at 1200 rev/min?

A $1.50 \mathrm{~kg}$ grinding wheel is in the form of a solid cylinder of radius $0.100 \mathrm{~m}$. $(a)$ What constant torque will bring it from rest to an angular speed of $1200 \mathrm{~rev} / \mathrm{min}$ in $2.5 \mathrm{~s}$ ? $(b)$ Through what angle has it turned during that time? $(c)$ Use Eq: " $W=\tau_z\left(\theta_2-\theta_1\right)=\tau_z \Delta \theta$ " to calculate the work done by the torque. $(d)$ What is the grinding wheel's kinetic energy when it is rotating at $1200 \mathrm{~rev} / \mathrm{min}$ ? Compare your answer to the result in part $(c)$.

A $2.80$-kg grinding wheel is in the form of a solid cylin- der of radius $0.100$ m.
(d) What is the grind- ing wheel's kinetic energy when it is rotating at $1200$ rev$/$min? Compare your answer to the result in part (c).

A $2.80$-kg grinding wheel is in the form of a solid cylin- der of radius $0.100$ m. (a) What constant torque will bring it from rest to an angular speed of $1200$ rev$/$min in $2.5$ s?

A $2.80$-kg grinding wheel is in the form of a solid cylin- der of radius $0.100$ m.
(b) Through what angle has it turned during that time?

The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center. When the skater's hand and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled, hollow cylinder. His hans and arms have a combined mass of 8.0 kg. When outstretched, they span 1.8 m; when wrapped, they form a cylinder of radius 25 cm. The moment of inertia about the rotation of the remainder of his body is constant and equal to 0.40 kg $\cdot$ m$^2$. If his original angular speed is 0.40 rev/s, what is his final angular speed?

A small block on a frictionless, horizontal surface has a mass of 0.025 kg. It is attached to a massless cord passing through a hole in the surface. The block is originally revolving at a distance of $0.300 \mathrm{~m}$ from the hole with an angular speed of $1.75 \mathrm{rad} / \mathrm{s}$. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to $0.150 \mathrm{~m}$. Model the block as a particle.

a) Is the angular momentum of the block conserved? Why or why not?

b) What is the new angular speed?

c) Find the change in kinetic energy of the block.

d) How much work was done in pulling the cord?

A small block of mass m on a horizontal frictionless surface is attached to a horizontal spring that has force constant k. The block is pushed against the spring, compressing the spring a distance d. The block is released, and it moves back and forth on the end of the spring. During its motion, what is the maximum speed of the block?

A small block of mass $m_1=0.500 \mathrm{~kg}$ is released from rest at the top of a curve-shaped frictionless wedge of mass $m_2=3.00 \mathrm{~kg}$, which sits on a frictionless horizontal surface as in Figure P9.60a. When the block leaves the wedge, its velocity is measured to be $4.00 \mathrm{~m} / \mathrm{s}$ to the right, as in Figure P9.60b. What is the velocity of the wedge after the block reaches the horizontal surface?

A 2.00-kg rock has a horizontal velocity of magnitude 12.0 m/s when it is at $v=12.0 \mathrm{~m} / \mathrm{s}$ point $P$ in the given figure. If the only force acting on the rock is its weight, what is the rate of change (magnitude and direction) of its angular momentum at this instant?

A 2.00 kg rock has a horizontal velocity of magnitude 12.0 m/s when it is at point P in the figure below. At this instant, what are the magnitude and direction of its angular momentum relative to point O?

A 2.00-kg rock has a horizontal velocity of magnitude 12.0 m/s when it is at $v=12.0 \mathrm{~m} / \mathrm{s}$ point $P$ in the given figure. At this instant, what are the magnitude and direction of its angular momentum relative to point $O$?