Intro to Torque Practice Problems

A horizontal thin rod is free to rotate about point O. Point O is considered the origin of the x-y plane. The point of application of the force is located at x = 1.5 m, y = 1 m. If the force has a magnitude of 80.0 N and is directed 30º north of east, determine the net torque about O.

You are using a long wrench to loosen a wheel nut. The wrench is located in the x-z plane and the nut is considered the origin of the Cartesian frame. The point of application of the exerted force is located at x = - 1 m, z = 0.25 m from the nut. The applied force in unit-vector notation is given as F = 100 i + 60 k. Determine the position vector r in terms of i and k at the point of application of the force.

To open a door, you exert a force at a point with a position vector r= 2 (m) i - 3 (m) j with respect to the hinge. The exerted force is given in unit-vector notation as F= 15 N i - 10 N j. The hinge is located at the origin of the Cartesian plane. In a graphic, draw the position vector r, the force F, and the origin.

When tightening the wheel nut on a bicycle, a cyclist applies a force of 125 N on the shaft of the spanner. The force is applied 25 cm from the nut. i) What is the highest torque the cyclist can produce by applying this force, and ii) with what angle with respect to the shaft the force should be exerted?

When tightening a bolt, a worker pushes on a wrench with a force of 90 N at a distance of 20 cm from the center of the bolt. The force makes an angle of 30 with the handle as shown in the image. How much torque, relative to the center of the bolt, is the worker exerting?

A slender rod of length L = 6 m is pivoted about one end. A 5 N force is applied 3 m from the pivot and perpendicular to the rod as shown in the image. The force and the rod are both located in the plane of the page. i) The magnitude and ii) direction of the torque about the pivot are:

A ball is launched so that it rolls down an inclined surface without slipping. The surface is inclined at an angle θ from the horizontal. If the ball is treated like a uniform solid sphere, determine the least possible value of the static friction coefficient needed to prevent the ball from slipping.

A hollow ball is essentially a hollow, spherical shell. If a ball of mass 4.40 kg is rolling down a 29.0° incline without slipping, what is its acceleration? 

A hollow ball of mass m is rolling down an inline without slipping. The incline plane angle is θ. How does doubling mass to 2m affect the ball's acceleration, friction, and least friction coefficient needed to hinder slipping?

A hollow sphere of mass 3.2 kg is released to roll down an incline leading to a raised floor. If the surface slopes at 31.0° above the horizontal, what friction force and minimum friction coefficient will prevent the ball from slipping?

A rectangular plate rotates about an axis passing through point A (x_A, y_A) as shown in the figure. The two forces acting on the plate produce a net torque of magnitude 2.3 N•m. Calculate x_A.

A sphere placed in a Cartesian frame at the position (1.5 m, 2.5 m, 0) is subject to a force F= -3 î N. Find the torque produced by F about the point O (0, 0, 0).

A 59-kg cyclist applies full force on each pedal while ascending a slope, with the pedals moving in a circular path of 18 cm radius. Determine what the highest value of torque that will be produced is.

A projectile is thrown in the air. Its location is given by R̄ = ( 3.00î + 2.20ĵ + 4.00k̂)m, and the total force acting on is given by F̅ = (9.00ĵ + 2.00k̂) N. Calculate the torque acting on the projectile about the origin of the coordinate system.

How can a 59-kg cyclist exert more torque while ascending a slope if he puts all his weight on each pedal? Given the pedals move in a circular path with a radius of 18 cm.

The screws on a machine's cylinder head requires 74.0 m•N of torque to be properly fastened to the cylinder head. Given that a spanner is 29.0 cm in length, what perpendicular force must be applied to the spanner at its end by a technician in order to properly fasten the screw?

Estimate the force applied by a spanner near each of the six points of the screws on a machine's cylinder head that need to be fastened with 74 m•N torque and the six-sided screw head is 16 mm across.

What torque does an artist exert on a turntable while molding a vase at 1.7 rev/s with a frictional force of 1.6 N between his hands and clay? Given the vase diameter is 13.0 cm and the moment of inertia is 0.13 kg•m².

During extreme weather, what torque does a force of F = (± 2.6 î - 4.2 ĵ) kN exert on a billboard sign at its center of mass about the base O?

A marble ball attached to a string is revolving counterclockwise in a horizontal circle of radius R_o with uniform angular acceleration α. The position vector r of the marble ball is given by: r̄ = î R_o cos Φ + ĵ R_o sin Φ where Φ = ω_it + (1/2)αt², where ω_i denotes the initial angular velocity of the marble ball and t is the time elapsed. Given that the mass of the marble ball is m, using τ̅ = r̄ × F̅, find the torque acting on it. Hint: First find the tangential acceleration a_t of the marble ball.

A disk is centred in a xy-coordinate system, rotating about the z-axis. A force of 216 N is applied within the xy-plane at a point 29.0 cm from the x-axis and 33.6 cm from the y-axis, making a 34.0° angle with the x-axis. What is the magnitude and direction of the torque generated around the z-axis?