A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the elbow joint as well as other movements. If the linear velocity of the ball relative to the elbow joint is 20.0 m/s at a distance of 0.480 m from the joint and the moment of inertia of the forearm is 0.500 kg $\cdot$ m$^2$ , what is the rotational kinetic energy of the forearm?

Read the Case Report presented below. Choose the correct answer to each question.

When completing required patient documentation, you would likely abbreviate your job title. Which abbreviation would you use? a. PTA b. COTA c. OT d. PT

A gyroscope slows from an initial rate of 32.0 rad/s at a rate of 0.700 rad/s$^2$ . (a) How long does it take to come to rest? (b) How many revolutions does it make before stopping?

While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.75 kg-m² and its rotational kinetic energy is 175 J. (a) What is the angular velocity of the leg? (b) What is the velocity of tip of the punter's shoe if it is 1.05 m from the hip joint?

(a) Calculate the angular momentum of an ice skater spinning at 6.00 rev/s given his moment of inertia is 0.400 kg $\cdot$ m$^2$ . (b) He reduces his rate of spin (his angular velocity) by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia if his angular velocity decreases to 1.25 rev/s. (c) Suppose instead he keeps his arms in and allows friction of the ice to slow him to 3.00 rev/s. What average torque was exerted if this takes 15.0 s?

A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the elbow joint as well as other movements. If the linear velocity of the ball relative to the elbow joint is $20.0 \mathrm{~m} / \mathrm{s}$ at a distance of $0.480$ $\mathrm{m}$ from the joint and the moment of inertia of the forearm is $0.500 \mathrm{~kg}-\mathrm{m}^2$, what is the rotational kinetic energy of the

In lacrosse, a ball is thrown from a net on the end of a stick by rotating the stick and forearm about the elbow. If the angular velocity of the ball about the elbow joint is 30.0 rad/s and the ball is 1.30 m from the elbow joint, what is the velocity of the ball?

Consider the 12.0 kg motorcycle wheel. Assume it to be approximately an annular ring with an inner radius of 0.280 m and an outer radius of 0.330 m. The motorcycle is on its center stand, so that the wheel can spin freely. (a) If the drive chain exerts a force of 2200 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? (b) What is the tangential acceleration of a point on the outer edge of the tire? (c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?

The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of $2.00\times 10^3$ N with an effective perpendicular lever arm of 3.00 cm, producing an angular acceleration of the forearm of 120 rad/s$^2$ . What is the moment of inertia of the boxer's forearm?

What is the final velocity of a hoop that rolls without slipping down a 5.00-m-high hill, starting from rest?

Everyday application: Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50 m/s$^2$ , what is the angular acceleration of the yo-yo? (b) What is the angular velocity after 0.750 s if it starts from rest? (c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acceleration of a point on its edge?

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. a. What is its angular acceleration in rad/s²? b.What is the tangential acceleration (in m/s²) of a point 10.00 cm from the axis of rotation? c. What is the radial acceleration in m/s²? and in multiples of g of this point at full rpm?

A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. She produces an angular acceleration of 30.00 rad/s$^2$ and her lower leg has a moment of inertia of 0.750 kg $\cdot$ m$^2$ . What is the force exerted by the muscle if its effective perpendicular lever arm is 1.90 cm?

A 200-g steel ball is tied to a 2.00-m "massless" string and hung from the ceiling to make a pendulum, and then, the ball is brought to a position making a 30° angle with the vertical direction and released from rest. Ignoring the effects of the air resistance, find the speed of the ball when the string (a) is vertically down, (b) makes an angle of 20° with the vertical and (c) makes an angle of 10° with the vertical.