A 8.49 -m ladder with a mass of 23.5 kg lies flat on the ground. A painter grabs the top end of the ladder and pulls straight upward with a force of 242 N. At the instant the top of the ladder leaves the ground, the ladder experiences an angular acceleration of 1.62rad/s2 about an axis passing through the bottom end of the ladder. The ladder's center of gravity lies halfway between the top and bottom ends. (a) What is the net torque acting on the ladder? (b) What is the ladder's moment of inertia?

A dragster starts from rest and accelerates down a track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 358 m, the angular speed of the wheels is 289 rad/s. Determine (a) the linear speed of the dragster and (b) the magnitude of the angular acceleration of its wheels.

A machine part rotates at an angular speed of 0.066 rad/s; its speed is then increased to 2.3 rad/s at an angular acceleration of 0.80 rad/s2. (a) Find the angle through which the part rotates before reaching this final speed. rad (b) If both the initial and final angular speeds are doubled and the angular acceleration remains the same, by what factor is the angular displacement changed? by a factor of 2 by a factor of 4 by a factor of 16 The angular displacement doesn't change.

A metal hoop lies on a horizontal table, free to rotate about a fixed vertical axis through its center while a constant tangential force applied to its edge exerts a torque of magnitude 1.75 x 10-2 N · m for 3.00 s. HINT (a) Calculate the magnitude of the hoop's change in angular momentum (in kg · m2/s). |kg - m²/s (b) Find the change in the hoop's angular speed (in rad/s) if its mass and radius are 0.270 kg and 0.180 m, respectively. rad/s

A small grinding wheel has a moment of inertia of 4.0 x 10-5 kg ⋅ m2. What net torque must be applied to the wheel for its angular acceleration to be 150 rad/s2?

The rotor of a helicopter is gaining angular speed with constant angular acceleration. At t = 0 it is rotating at 1.25 rad/s. From t = 0 to t = 2.00 s, the rotor rotates through 8.00 rad. (a) What is the angular acceleration of the rotor? (b) Through what angle (in radians) does the rotor rotate from t = 0 to t = 4.00 s?

An automobile engine can produce 200 N · m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.

A gymnast on the uneven parallel bars is at rest, tipped at a 45° angle from the vertical. The distance from her hands to her feet is 1.8 m. If we model her body as having a uniform cross section and assume that her center of gravity is midway between her hands and her feet, what is her initial angular acceleration?

A 10 kg cylindrical barrel with a radius of 0.5 m rotates about a vertical axis of rotation without displacing with an initial angular velocity of 4 rad/s. The rotational inertia of the cylindrical barrel is 0.3mr2 and rain begins to fill the barrel with water as its rotating. If the barrel accumulates 4 kg of water, calculate the new angular velocity of the barrel.

A uniform drawbridge must be held at a 37° angle abovethe horizontal to allow ships to pass underneath. The drawbridge weighs45,000 N and is 14.0 m long. A cable is connected 3.5 m from thehinge where the bridge pivots (measured along the bridge) and pullshorizontally on the bridge to hold it in place. What is the angular speed of the drawbridge as it becomes horizontal?